THE  UNIVERSITY 

OF  ILLINOIS 

LIBRARY 

630.7 
II6b 


A6RI6ULTUBAL 
UIBABY 


UNIVERSITY  OF  ILLINOIS 

Agricultural  Experiment  Station 


BULLETIN  No.  245 


RELATION  BETWEEN  PERCENTAGE 

FAT  CONTENT  AND  YIELD 

OF  MILK 

Correction  of  Milk  Yield  for  Fat  Content 

BY  W.  L.  GAINES  AND  F.  A.  DAVIDSON 


I 


UKRANA,  ILLINOIS,  JUNE,  192.3 


CONTENTS  OF  BULLETIN  No.  245 

PAGE 

INTRODUCTION 577 

SOURCE   OF   DATA 578 

HYPOTHESIS   579 

PRESENTATION  580 

The  Constant  Energy  Curve 581 

The  Logarithmic  Curve    583 

Comparisons 583 

The  Constant  Fat  Curve 583 

Age  Correction   583 

DISCUSSION 584 

The  Coefficient   of  Correlation 584 

Holstein  Cow  Testing  Association  Records 584 

Jersey  Cow  Testing  Association  Records 585 

Nature  of  Advanced  Registry  Selection 586 

Jersey  Register  of  Merit  Long-Time  Records 588 

Jersey  Register  of  Merit  Seven-Day  Records 589 

Guernsey  Advanced  Register  Records 589 

Ayrshire  Advanced  Registry  Records 589 

Brown  Swiss  Register  of  Production  Records 590 

Holstein-Friesian  Advanced  Register  Long-Time  Records 591 

Holstein-Friesian  A.  R.  O.  Seven-Day  Records 592 

Summary  of   Evidence 593 

CORRECTION  OF  MILK  YIELD  FOR  FAT  CONTENT 594 

Derivation  of  Formula 594 

Application  of  Formula 594 

SUMMARY 597 

CONCLUSIONS 598 

LITERATURE  CITED   598 

TABLES  .  ..599-621 


RELATION  BETWEEN  PERCENTAGE  FAT 
CONTENT  AND  YIELD  OF  MILK 

Correction  of  Milk  Yield  for  Fat  Content 

BY  W.  L.  GAINES,  CHIEF  IN  MILK  PRODUCTION,  AND 
F.  A.  DAVIDSON,  FIRST  ASSISTANT  IN  DAIRY  HUSBANDRY 

INTRODUCTION 

Among  dairymen,  it  is  a  matter  of  common  observation  that,  in 
general,  the  milk  yields  of  cows  tend  to  vary  inversely  with  the  per- 
centage fat  content  of  the  milk.  Various  statistical  investigations,  by 
the  method  of  correlation,  support  this  observation.  Such  investiga- 
tions have  shown  the  existence  of  a  significant  negative  coefficient  of 
correlation  between  the  two  variables,  percentage  fat  content  of  the 
milk  and  yield  of  milk.  The  present  study  is  a  further  analysis  of 
this  relation  based  on  23,302  records  of  the  milk  and  fat  production 
of  cows.  It  purposes  to  show  the  nature  of  the  relation  between  per- 
centage fat  content  of  the  milk  and  yield  of  milk ;  and  to  formulate 
a  method  of  correcting  milk  yield  to  equate  for  the  influence  of  fat 
content. 

The  dairy  cow  occupies  her  position  in  our  agriculture  primarily 
as  a  producer  of  milk.  Cows  are  highly  variable  in  milk  yield;  and 
this  variability  is  a  large  factor  in  the  immediate  economy  of  milk 
production,  and  of  great  import  in  the  possible  future  dairy  develop- 
ment of  the  cow.  But  variability  in  milk  yield  is  affected  by  many 
factors,  and  if  the  milk  yield  of  a  cow  is  to  be  used  as  an  indication 
of  her  position  on  the  scale  of  merit  with  reference  to  immediate 
economy  and  future  development,  it  is  desirable  to  distinguish  the 
factors  affecting  milk  secretion,  and  to  have  a  measure  of  the  effect  of 
each.  The  advanced  registry*  records  of  the  dairy  breeds  usually 
list  three  such  factors,  each  of  which  is  very  potent  in  its  influence 
on  milk  yield;  viz.,  time  (length  of  record),  percentage  of  fat,  and 
age  of  cow.** 


*The  term  advanced  registry  is  used  frequently,  as  here,  in  a  general  sense 
to  apply  to  any  of  the  breeds. 

** Among  other  factors  affecting  milk  yield  the  list  following  may  be  sug- 
gestive: food  supply  (amount,  character)  ;  body  food  reserves  (body  fat,  mineral 
store);  growth  of  cow;  size  of  cow;  pregnancy  preceding  lactation  (sex  of 
fetus,  sire  of  fetus,  normal  term,  premature  or  delayed  delivery,  birth  weight)  ; 
pregnancy  during  time  of  lactation;  ovariotomy;  frequency  of  milking;  char- 
acter of  milking ;  previous  development  (exercise  and  training  of  the  mammary 
function  at  preceding  lactations);  physical  exercise;  comfort  (temperature, 
flies,  etc.).  Undoubtedly  some  of  these  are  of  considerable  importance,  while 
others  may  have  little  or  no  influence.  Of  the  many  important  factors  it  is 
remarkable  that  we  have  had  an  adequate  measure  of  the  influence  of  only  one, 
that  of  age.  It  is  hoped  the  data  following  will  supply  a  measure  for  one  other, 
that  of  percentage  fat  content  of  the  milk. 

577 


578  BULLETIN  No.  245  [June, 

The  age  of  a  cow  has  long  been  recognized  as  a  factor  affecting  the 
milk  yield.  The  advanced  registry  system  when  first  established  in 
1885  took  account  of  this  fact.  Various  data  have  been  published 
from  time  to  time  showing  the  absolute  or  relative  milk  yields  by  cows 
at  varying  ages.  Gowen1  has  shown  that  the  relation  between  these 
two  variables — age  and  yield — may  be  closely  expressed  by  a  logarith- 
mic curve,  and  has  given  the  equations  for  the  curves  for  the  Hoi- 
stein,  Jersey,  and  Guernsey  breeds.  These  equations  have  been  found 
valuable  in  this  laboratory  in  equating  the  milk  yields  of  cows  so  as 
to  make  the  yields  directly  comparable  in  so  far  as  the  age  factor  is 
concerned.* 

SOURCE  OF  DATA 

The  data  used  in  this  study  have  been  taken  from  the  records  of 
cow  testing  associations  in  Illinois  (unpublished**)  and  the  published 
records  of  the  Holstein-Friesian  Association,  the  American  Jersey 
Cattle  Club,  the  American  Guernsey  Cattle  Club,  the  Ayrshire 
Breeders'  Association,  and  the  Brown  Swiss  Breeders'  Association. 

The  records  of  the  cow  testing  associations  include  only  two  breeds 
— Holstein  and  Jersey — in  numbers  large  enough  to  be  of  value  for 
present  purposes.  The  Holstein  records  are  of  both  grades  and  .pure- 
breds,  located  in  commercial  dairy  herds  in  the  whole-milk  districts 
of  Illinois.  The  records  used  are  from  those  associations  only  that 
are  known  to  have  had  competent  and  reliable  testers  in  charge,  and 
whose  members  sold  whole  milk  at  about  the  same  price  (price  being 
a  factor  in  the  amount  of  feed  given  the  cows,  and  consequently  a 
factor  in  milk  yield).  Very  little  advanced  registry  testing  was 
practiced. 

The  Jersey  records  are  of  both  grades  and  pure-breds,  obtained  in 
one  association  over  a  period  of  five  years.  The  number  of  cows  in- 
volved is  consequently  less  than  the  number  of  records  used.  Whole 
milk  was  sold,  the  market  paying,  however,  in  exact  proportion  to 
the  fat  content  of  the  milk.  The  quality  of  the  cows  and  the  condi- 
tions under  which  the  records  were  made  were  similar  to  those  of  the 
Holsteins.  No  advanced  registry  testing  was  practiced. 

*The  use  of  corrections  is  common  in  the  physical  sciences.  When  the 
chemist  determines  the  volume  of  a  gas,  he  corrects  his  measurement  to  certain 
standard  conditions;  he  makes  a  correction  for  temperature,  a  second  correction 
for  barometric  pressure,  and  a  third  correction  for  the  tension  of  aqueous  vapor. 
Biological  corrections  of  the  kind  under  consideration  here  are  just  as  much 
needed  and  just  as  useful  as  those  used  in  the  physical  sciences.  In  many  cases 
it  is  impossible  to  standardize  the  cause  of  variation,  and  in  such  cases  the  only 
recourse  is  to  standardize  the  effect  thru  the  use  of  a  correction  factor.  The 
determination  of  biological  corrections  is  complicated  by  the  multiplicity  of  re- 
actions occurring  simultaneously  in  the  living  organism,  and  this  condition  may 
subject  the  determination  to  error  and  to  the  necessity  of  revision  as  addi- 
tional evidence  accumulates. 

**The  writers  acknowledge  the  courtesy  of  Professor  C.  S.  Rhode  of  the 
Dairy  Department,  University  of  Illinois,  in  supplying  part  of  these  records. 


W2S}  RELATION  BETWEEN  FAT  CONTENT  AND  MILK  YIELD  579 

The  records  of  the  breed  associations  are  the  well-known  advanced 
registry  records.  They  need  no  explanation  here,  but  it  may  be  in 
point  to  recall  that  they  are  made  under  a  wide  range  of  conditions, 
and  that  in  some  cases  no  expense  in  feed,  care,  and  manipulation  is 
spared  in  order  to  secure  a  maximum  recorded  production.  The  goal 
of  advanced  registry  testing  (except  possibly  the  Ayrshire)  is  based 
on  the  fat  record  rather  than  on  the  milk  record.  Consequently,  there 
is  a  stimulus  toward  any  manipulation  that  increases  the  real  or  ap- 
parent fat  percentage  as  well  as  the  yield  of  milk. 

It  is  very  seldom  that  all  the  cows  of  a  herd  are  included  in  the 
advanced  registry  system,  whereas  it  is  very  rarely  that  they  are 
not  all  included  in  the  cow  testing  association  system.  As  compared 
with  the  cow  testing  association  records,  the  advanced  registry  rec- 
ords represent  a  higher  capacity  portion  of  the  total  population,  pro- 
ducing under  conditions  nearer  the  optimum  for  maximum  production. 

HYPOTHESIS 

Preliminary  study  suggested  that  the  relation  between  the  per- 
centage fat  content  of  the  milk  and  the  yield  of  milk  is  simple  and 
logical;  namely,  (1)  the  solids-not-fat,  as  well  as  the  fat  itself,  are 
concerned  in  the  relation;  (2)  the  relation  depends  on  the  energy 
value  of  the  fat  and  the  solids-not-fat,  rather  than  directly  on  the 
amount  of  solids  present;  (3)  the  energy  value  of  the  total  solids  of 
the  milk  is  constant,  if  all  factors  which  affect  milk  yield,  other  than 
the  solids  content,  are  compensated. 

If  the  above  is  in  fact  the  case,  the  physiological  relation  between 
the  two  variables  fat  percentage  and  milk  yield  is  revealed,  and  a  base 
is  established  from  which  to  correct  milk  yield  for  the  influence  of 
fat  content.  If  the  percentage  fat  content  of  the  milk  is  a  factor 
affecting  milk  yield  according  to  a  definite  physiological  relation,  and 
this  relation  can  be  expressed  mathematically,  the  use  of  such  mathe- 
matical expression  in  the  correction  of  milk  yield  for  fat  content  is 
justified  from  a  physiological  standpoint.  Indeed,  correction  by  such 
a  method  is  preferable  to  the  use  of  an  expression  describing  the  rela- 
tion found  in  the  advanced  registry  data  because  advanced  registry 
selection  and  practices  may  to  some  extent  distort  the  true  relation. 
For  the  purpose  of  the  present  study,  the  following  hypothesis  is 
therefore  adopted: 

The  milk  yield  of  cows  with  varying  fat  percentages  is  such  that 
the  total  energy  value  of  the  milk  is  constant  if  the  effects  of  all  fac- 
tors other  than  composition  are  equalized. 

That  is,  by  way  of  further  explanation,  there  are  many  things 
which  influence  the  amount  of  milk  that  cows  produce;  for  example, 
the  fat  percentage  of  the  milk,  length  of  record,  the  individuality  of 
the  cow,  age,  feed,  and  so  forth.  The  influence  of  fat  percentage 


580  BULLETIN  No.  245  [June, 

(or  rather,  composition  as  measured  by  fat  percentage)  is  the  par- 
ticular factor  now  under  study ;  and  the  proposition  of  the  hypothesis 
is  that  if  the  effects  of  each  of  the  other  factors  are  made  equal  for 
each  cow,  the  energy  value  of  the  total  milk  produced  by  each  cow 
will  be  the  same — a  constant.  The  influence  of  fat  percentage  on  yield 
is,  according  to  the  hypothesis,  a  function  of  the  energy  value  of  the 
fat  plus  the  energy  value  of  the  solids-not-fat  present  in  the  milk; 
and  the  influence  is  measured  directly  by  the  energy  value  of  the 
solids.  The  milk  yield  must,  by  the  hypothesis,  be  inversely  pro- 
portional to  the  energy  value  of  the  solids  per  unit  of  milk. 

Now,  in  order  to  subject  the  hypothesis  to  test  it  is  necessary  to 
meet  the  condition  that  all  factors  except  composition  be  equalized. 
It  is  impossible  to  do  this  directly  for  all  factors.  Indirect  methods, 
based  on  statistical  principles  must  be  used. 

If  we  take  a  large  number  of  cows,  representative  of  the  same 
breed,  working  under  similar  conditions,  and  separate  them  into  classes 
on  the  basis  of  the  percentage  fat  content  of  their  milk,  and  deter- 
mine the  average  milk  yield  of  each  class,  we  may  assume  that,  as 
between  the  averages  so  obtained,  all  factors  in  milk  yield  are  equal- 
ized, except  the  one  on  which  the  classification  is  based.  On  statistical 
principles,  which  need  not  be  elaborated  here,  this  will  be  true,  within 
a  certain  probability  of  error,  except  as  to  factors  which  are  also  cor- 
related with  fat  percentage.  The  factor  solids-not-fat  is  such  an  ex- 
ception, and  that  is  why  it  is  treated  together  with  the  fat.  What  we 
really  have  to  consider  is  the  influence  of  composition  on  milk  yield. 

There  are  undoubtedly  some  other  factors,  such  as  the  size  of  the 
cow,  which  are  correlated  with  fat  percentage,  but  the  net  effect  of 
all  such  factors  is  regarded  as  being  so  small  as  to  be  negligible. 

The  hypothesis  is  concerned  with  the  energy  value  of  the  milk 
solids,  but  the  records  used  give  only  the  amount  of  milk  and  the  fat 
content.  It  is  necessary,  therefore,  to  estimate  the  energy  value,  and 
the  method  and  justification  for  this  will  appear  shortly. 

It  is  on  the  principles  outlined  above  that  the  hypothesis  was  sug- 
gested by  study  of  the  data.  On  the  same  principles  the  validity  of 
the  hypothesis  is  put  to  test  in  the  following  pages,  representative  data 
from  all  the  records  available  being  used. 

PRESENTATION 

The  records  used  give  the  fat  percentage  to  the  closest  second 
decimal,  and  the  milk  yield  in  pounds  and  tenths.  Each  group  of 
records  is  arranged  in  a  correlation  table  (see  pages  599  to  621),  class 
intervals  of  0.1  for  fat  percentage  and  1,000  pounds  for  milk  yield 
(20  or  50  pounds  for  the  seven-day  records)  being  used.  The  coeffi- 


192S]  RELATION  BETWEEN  FAT  CONTENT  AND  MILK  YIELD  581 

cients  of  correlation  and  other  constants  have  been  derived  by  standard 
methods  and  are  given  in  Table  21.  The  mean  milk  yields  of  the 
several  fat  percentage  classes  have  been  computed  from  the  corre- 
lation tables  and  are  given  in  tabular  form  (pages  600  to  618)  and  in 
the  accompanying  graphs.  Included  with  these  latter  data,  in  both 
tables  and  graphs,  are  two  other  sets  of  data :  first,  the  corresponding 
milk  yields  calculated  from  a  fitted  curve  of  constant  energy,  and  the 
deviations  of  the  observed  from  the  calculated  values;  second,  the 
corresponding  milk  yields  calculated  from  a  fitted  logarithmic  curve, 
and  the  deviations  of  the  observed  from  the  calculated  values. 

The  Constant  Energy  Curve. — It  is  well  known  that  the  solids- 
not-fat  content  of  normal  milk  varies  with  the  fat  content  in  a 
very  definite  ratio.  Gowen2  finds,  in  Holstein  cows,  a  correlation  of 
-f-  .8991  ±  .0071  between  these  two  constituents ;  indicating  that  the 
solids-not-fat  content  of  milk  may  be  determined  with  reasonable 
accuracy  from  the  fat  content.  The  energy  value  of  milk  fat  and  of 
solids-not-fat  is>  also  definite  and  well  established.  Stocking  and 
Brew3  working  with  extensive  data  compiled  from  various  sources 
have  prepared  a  table  which  shows  these  several  relations.*  From 
their  table  we  derive  :** 


*Overman*  also  gives  data  which  bear  on  this  relation.  He  has  compiled 
several  thousand  complete  analyses  of  milk  of  stated  known  purity  and  studied 
them  from  the  standpoint  of  the  food  value  of  milk  of  varying  percentage  fat 
content.  His  data  cover  a  range  of  fat  percentage  from  3  to  7,  and  show  a  linear 
relation  between  fat  percentage  and  food  (energy)  value  per  quart  of  milk.  The 
curve  is  in  excellent  agreement  With  that  of  Stocking  and  Brew  as  to  direction  but 
somewhat  lower  (about  7  percent)  in  absolute  values.  The  difference  in  absolute 
values  is  accounted  for  in  large  part  by  a  variance  in  the  energy  values  used  by 
the  two  authorities  for  fat  and  solids-not-fat. 
** Symbols  are  used  as  follows: 

D  =  deviation  of  observed  from  calculated  milk  yield,  in  pounds. 

E  —  energy  of  milk  solids,  in  large  calories. 

ECM  =  milk  yield  corrected  for  energy  value  to  4  percent  fat. 

f  =  frequency. 

F  =  milk  fat,  in  pounds. 

FCM  —  milk  yield  corrected  for  fat  to  4  percent  fat. 

F-SCM  =  milk  yield  corrected  for  fat  and  solids  to  4  percent  fat. 

M  =  milk,  in  pounds. 

•»rci  S(4-D) — S( — D) 

ME  —  mean  error,        v  ~ — : ±_1 '— 

n 

Me  =  milk  yield,  in  pounds,  calculated  from  constant  energy  curve. 
M,  =.  milk  yield,  in  pounds,  calculated  from   constant   fat   curve. 
M,  =  milk  yield,  in  pounds,  calculated  from  logarithmic  curve. 
M0  —  mean  milk  yield,  in  pounds,  observed. 
n  =  number  of  values, 
r  =i  coefficient  of  correlation.  -, 

(y  D2 

EE  =  root  mean  square  error,  A ,' 

\    n 

S-N-F  —  solids-not-fat,  in  pounds.  . 

s-n-f  =i  percentage  solids-not-fat  content  of  milk.  *P**£ 

t  =  percentage  fat  content  of  milk.  .^ 

S  =  summation. 


582  BULLETIN  No.  245  [June, 

s-n-f  =  7.1  -f  0.4  t 

E    =  132.06  M  -f  4964  F   (and,  since  F  =  .01  Mt) 
=  132.06  M  -f  49.64  Mt 
=  49.64  M  (2.66  -f  t) 

By  hypothesis,  E  is  constant,  say  49.64a  (a  being  a  constant  the 
value  of  which  is  to  be  determined).  Then,  for  the  amount  (pounds) 
of  milk,  Me,  necessary  to  satisfy  this  value  of  E,  we  have: 

49.64  Me  (2.66  +  1)  =  49.64a 
and, 

M  -  a 

=  2.66  -ft 

This  curve  is  arbitrarily  so  fitted  to  the  observations  that  at  values 
of  t  corresponding  to  those  of  the  observations, 

SM«  =  3M. 

Hence, 


or, 


and, 

2Mn 


a=- 


*  2.66  -f  t 

The  method  of  fitting  causes  the  sum  of  the  plus  deviations  and 
the  sum  of  the  minus  deviations  to  be  equal  in  value.     It  does  not 

2   (_I_J))   _  2   (  _  D) 

necessarily  reduce  either  the  mean  error,  —  —  ,  or  the 


2  D2 
root  mean-square  error,  ^/  -  1  to  a  minimum.  However,  the  method 

answers  for  present  purposes.  The  constants  are  given  in  Table  22. 
The  reader  should  bear  in  mind  that  the  energy  curve  is  an  ex- 
pression of  the  hypothesis.  While  it  is  "fitted"  to  the  observations, 
this  "fitting"  only  adjusts  the  mean  level  of  the  curve  to  the  mean 
level  of  the  observations  of  milk  yield.  Its  shape  and  general  direc- 
tion are  fixed  and  inflexible.  If  it  conforms  to  the  observations,  that 
conformity  is  evidence  that  fat  percentage  affects  milk  yield  and  that 
the  effect  of  fat  percentage  on  milk  yield  is  measured  directly  by  the 
energy  value  of  the  milk  solids.  If  the  energy  curve  conforms  to  the 
observations,  it  is  evidence  in  support  of  the  validity  of  the  hypothesis. 


1923]  RELATION  BETWEEN  FAT  CONTENT  AND  MILK  YIELD  583 

The  Logarithmic  Curve. — In  general,  the  data  suggest  that  a  curve 
of  the  type  y  =  a-)-bx-(-c  Iog10  (x-|-a)  should  be  adapted  to  fit 
the  observations.  Further,  this  type  of  curve  has  been  found  appli- 
cable to  the  expression  of  many  biological  relations.  Consequently,  it 
has  been  used  here,  and  has  been  fitted  to  each  set  of  data  by  the 
method  of -moments,  using  Miner's5  equations  and  tables.  The  con- 
stants for  the  several  equations  are  given  in  Table  22.  The  logarithmic 
curve  is  used  purely  for  purposes  of  comparison. 

Comparisons. — The  graphs  (Figs.  1  to  10)  give  a  visual  impression 
of  how  well  the  observations  support  the  hypothesis:  first,  by  com- 
paring the  energy  curve,  which  represents  the  hypothesis,  with  the 
observations  themselves ;  second,  by  comparing  the  energy  curve  with 
the  fitted  logarithmic  curve.  A  further  comparison  with  the  logarith- 
mic curve  is  afforded  by  the  tabular  presentation  (see  pages  599  to  621) . 
Here  a  numerical  expression  of  the  fit  of  the  energy  curve  is  attempted 
by  giving,  for  both  curves,  the  mean  error,  and  the  root  mean-square 
error.  These  errors  are  given  also  in  the  graphs.  If  the  error  of  the 
energy  curve  is  not  greater  than  that  of  the  logarithmic  curve,  then, 
so  far  as  the  logarithmic  curve  is  a  guide,  the  observations  support 
the  hypothesis.  Likewise,  an  error  for  the  energy  curve  greatly  in 
excess  of  that  for  the  logarithmic  curve,  shows  a  lack  of  support. 
The  errors  for  the  several  sets  of  data  are  brought  together  in 
Table  23. 

The  Constant  Fat  Curve. — Since  a  fat  standard  is  used  as  the 
basis  of  admission  to  the  advanced  registry,  and  since  fat  yield  is  quite 
generally  used  as  a  measure  of  a  cow's  production,  it  has  seemed 
desirable  to  consider  the  yield  of  milk  required  for  a  constant  yield 

Q 

of  fat.     The  equation  for  the  curve  of  constant  fat  is  Mf  =— ,  and 

u 

this  curve  has  been  fitted  by  determining  a  after  the  same  manner 
as  in  the  energy  curve.  The  data  are  given  only  in  summary  form 
(Tables  22  and  23),  except  that  for  the  purpose  of  illustration  the 
curve  is  drawn  into  one  of  the  graphs  (Fig.  1). 

Age  Correction. — It  has  been  found  unnecessary  to  use  an  age- 
correction  factor  for  the  milk  yields,  except  in  two  cases  where  a 
comparatively  small  number  of  records  is  used.  For  a  limited  num- 
ber of  records  it  serves  to  smooth  the  data  materially,  and  would  prob- 
ably be  useful  in  smoothing  the  values  for  the  end  and  near-end  fre- 
quencies in  other  cases.  The  two  cases  corrected  are  the  Brown 
Swiss  and  the  early  Holstein  seven-day  records.  The  Brown  Swiss 
records,  as  published,  give  the  age  only  by  groups.  Yields  are  cor- 
rected to  age  of  maximum  yield  by  using  Gowen's1  equation  for  the 
Holstein  breed.  The  Holstein  seven-day  records  have  been  corrected 
to  the  age  of  8  years  9  months  by  using  data  given  by  Miner.5 


584  BULLETIN  No.  245  [June, 

DISCUSSION 

The  Coefficient  of  Correlation. — Table  21  shows  the  correlation 
between  fat  percentage  and  milk  yield  to  be  negative  in  every  case. 
The  coefficient  is  not  very  high  in  any  case  but  is  significant  in  every 
case.  The  correlation  for  the  Holstein  and  Jersey  cow  testing  asso- 
ciations (r  — — .198  ±  .012  and  — .212  ±  .021,  respectively)  have  the 
most  meaning  from  the  standpoint  of  the  normal  relation  between 
percentage  fat  content  and  yield  of  milk  because  the  populations  they 
represent  are  the  least  selected  of  any  of  the  groups. 

Advanced  registry  selection  (except  the  Ayrshire),  by  reason  of 
the  entrance  requirements,  tends  to  increase  the  negative  correlation. 
This  appears  prominently  in  the  case  of  the  Jersey  seven-day  records, 
where  r  =  — .506  ±  .026.  The  entrance  requirement  in  this  class  is 
twelve  pounds  of  fat  regardless  of  age.  Inspection  of  the  correlated 
distributions  (Table  7)  shows  that  a  considerable  part  of  the  total 
population  is  cut  off  in  the  upper  left  portion  (low  fat  percentage  and 
low  milk  yield).  The  effect  of  this  is  to  give  a  higher  negative  value 
to  r  than  would  be  obtained  from  a  distribution  representative  of  the 
whole  Jersey  population  (see  also  Fig.  A).  Exactly  the  same  prin- 
ciple opesates,  in  lesser  degree,  in  the  other  advanced  registry  groups, 
except  in  the  Ayrshire.  The  Ayrshire  standard  is  peculiar  in  that 
there  is  a  minimum  milk  requirement  besides  the  usual  fat  require- 
ment. The  effect  of  the  additional  milk  requirement  is  nil  at  values 
of  t  below  3.57^.29  (the  value  varying  with  age),  but  above  that 
point  the  milk  requirement  tends  to  give  a  positive  correlation.  There 
are  also  other  complications  (see  Roberts,6  page  73). 

The  low  value  of  r  is  caused  in  part  by  the  great  variability  in  milk 
yield,  due  to  the  inherent  quantitative  differences  in  the  function  of 
milk  secretion  and  to  the  extreme  susceptibility  of  this  function  to 
environmental  factors.  Everyone  knows,  of  course,  that  a  knowledge 
of  the  percentage  fat  content  of  a  cow's  milk  does  not  justify  an 
estimate  of  her  milk  yield.  But  the  fact  of  a  significant  correlation 
shows  that  there  exists  some  definite  relation  between  the  fat  per- 
centage and  the  mean  milk  yield  of  a  number  of  cows.  The  nature 
of  this  relation  is  brought  out  more  clearly  by  the  graphs  and  tables 
for  each  group  of  records. 

Holstein  Cow  Testing  Association  Records. — The  data  for  these 
records  are  found  in  Tables  1  and  2,  and  Fig.  1.  Survey  of  the  graph 
shows  that  the  energy  curve  is  very  nearly  coincident  with  the 
logarithmic  curve.  Its  mean  error  is  one  pound  greater,  and  its  root 
mean-square  error  six  pounds  less  than  for  the  logarithmic  curve.  If 
there  is  any  choice  between  the  two  it  would  seem  to  be  in  favor  of 
the  energy  curve,  either  on  the  basis  of  the  magnitude  of  the  errors 
or  the  general  impression  formed  by  study  of  the  graph. 


1923} 


RELATION  BETWEEN  FAT  CONTENT  AND  MILK  YIELD 


585 


The  curve  of  constant  fat  is  added  in  Fig.  1  for  the  sake  of  illus- 
tration. It  is  quite  obvious  that  fat  yield  is  not  an  equitable  measure 
of  production  within  the  classes  represented.  The  fat  curve  has  a 
mean  error  of  555  pounds  and  a  root  mean-square  error  of  775  pounds 
(Table  23),  or  nearly  double  that  of  the  energy  curve.  It  is  not  given 
in  the  data  for  the  remaining  records  since  it  bears  a  similar  relation 
to  the  energy  curve  in  all  cases. 


?- 

i. 

»„ 


waf/M 

osse*vATte4j  *f 


S3      SS       S7 


ffr  COMTCHT  Of  MILK 

FIG.  1. — RELATION  BETWEEN  FAT  PERCENTAGE  AND  MILK  YIELD:    HOLSTEIN- 

FRIESIAN  Cow  TESTING  ASSOCIATION  YEARLY  RECORDS 

2,773  records.     Data  from  Table  2,  page  600 

The  2,773  records  concerned  here  should  be  thoroly  representative 
of  the  Holstein  breed,  under  good  conditions  of  management,  in  herds 
dependent  primarily  upon  the  sale  of  milk  for  their  income.  The 
majority  of  the  cows  were  high  grades. 

It  will  be  noted  that  while  the  general  tendency  of  the  observa- 
tions is  plainly  in  the.  direction  of  the  energy  curve,  there  are  many 
rather  wide  deviations  from  it.  Toward  either  end,  where  the  fre- 
quencies are  small,  wide  fluctuations  are  natural.  But  even  with 
larger  frequencies  there  are  some  apparently  wide  deviations.  For 
example,  the  class  at  t  — 3.345  shows  a  deviation  of  132  pounds. 
Considering  the  337  records  of  this  class  by  themselves,  the  mean, 
7,384,  has  a  probable  error  of  79.6.  From  this  we  might  expect  a  de- 
viation of  132  about  once  in  five.  For  the  other  classes,  having  smaller 
frequencies,  the  chance  of  error  in  the  mean  would  be  still  greater. 
Consequently,  some  irregularity  in  the  observations  is  to  be  expected 
and  is  no  reason  for  discrediting  the  data. 

Jersey  Cow  Testing  Association  Records. — The  data  for  these  rec- 
ords appear  in  Tables  3  and  4,  and  Fig.  2.  The  observations  are  less 
regular  in  distribution  than  those  in  Fig.  1.  The  number  of  records 
is  much  smaller,  970,  and  the  number  of  cows  represented  still  smaller. 

Again,  the  energy  curve  is  practically  coincident  with  the  logar- 
ithmic curve.  Its  errors  are  greater  by  6  pounds  for  the  mean  and 


586 


BULLETIN  No.  245 


[June, 


1  pounds  for  the  root.    This  is  less  than  2  percent,  and  considering  the 
nature  of  the  data  is  very  close. 


!• 


c//>?,  ter  t  T.A. 


+6    4M     S.O     A*     **     M     S.e     6.0     ea      «4     Ce     SB 

far  CONTENT  or  MILK 


FIG.  2.  —  RELATION  BETWEEN  FAT  PERCENTAGE  AND  MILK  YIELD:    JERSEY 

Cow  TESTING  ASSOCIATION  YEARLY  RECORDS 

970  records.     Data  from  Table  4,  page  602 

.  The  records  of  the  Holstein  and  Jersey  cow,  testing  associations 
are  regarded  as  supporting  the  hypothesis  remarkably  well.  No 
similar  records  for  other  breeds  were  available  for  study.  We  have 
to  consider  next  the  advanced  registry  records,  but  before  doing  so  it 
is  necessary  first  to  discuss  the  nature  of  the  selection  effected  by  the 
requirements  for  admission  to  the  advanced  registry. 

Nature  of  Advanced  Registry  Selection.  —  Fig.  A  is  a  diagram  de- 
signed to  illustrate  the  nature  of  advanced  registry  selection.  It  is 
intended  to  represent  a  correlation  surface  for  fat  percentage  and 
milk  yield  for  a  very  large  number  of  cows  under  official  test  con- 
ditions. All  cows  above  the  line  AB  would  be  excluded  by  an  entrance 
requirement  of  360  pounds  of  fat,  and  all  cows  below  the  line  could 
qualify.  If  the  broken  line  represents  the  periphery  of  the  popula- 
tion, and  the  population  increases  in  density  with  some  uniformity 
toward  its  center,  then  it  is  clear  from  the  diagram  that  an  increasing 
proportion  of  cows  is  eliminated  as  we  go  from  higher  to  lower  fat 
percentage.  Since  it  is  the  poorest  grades  of  cows  that  are  eliminated, 
the  qualitative  effect  must  be  to  improve  the  mean  grade  of  those  left. 
And  improvement  would  increase  as  we  go  from  higher  to  lower  fat 
percentage,  because  of  the  increasing  proportion  of  the  population 
eliminated. 

The  proportion  of  a  total  population  that  would  fail  to  qualify 
for  the  advanced  registry  is  uncertain.  Roberts13  refers  to  98  Ayrshires 
which  were  tested  and  failed  to  qualify  (with  an  entrance  require- 
ment of  214.3  to  322  pounds  of  fat,  according  to  age)  presumably 
comparable  with  1,091  that  did  qualify.  Since  the  poorest  cows  are 
probably  not  tested  at-  all,  it  would  seem  that  advanced  registry  re- 
quirements would  exclude  at  least  10  percent  of  the  total  population 
if  all  were  tested. 


19*8] 


RELATION  BETWEEN  FAT  CONTENT  AND  MILK  YIELD 


587 


tr  CoM-rttrr  tr  MILK 


*/*> 
I 


B- 


FIG.  A. — ILLUSTRATING  THE  NATURE  OF  THE  SELECTION  EFFECTED  BY  A 

CONSTANT  FAT  PRODUCTION  REQUIREMENT 

The  broken  line  is  intended  to  represent  the  periphery  of  a  very 
large  cow  population.  The  line  AB  is  drawn  thru  the  points  correspond- 
ing to  360  pounds  of  fat.  Note  that  selection  is  more  severe  at  low  fat 
percentages  than  at  higher  fat  percentages.  The  figure  is  purely  dia- 
grammatic. 

On  the  basis  of  energy  yield,  the  nature  of  advanced  registry  selec- 
tion is  shown  clearly  by  Table  A.  The  table  shows  that  selection  be- 
comes increasingly  more  severe  in  going  from  higher  to  lower  fat 
percentages.  It  is  therefore  to  be  expected  that  the  mean  energy 
yield  shown  by  advanced  registry  records  will  be  greater  at  lower 
values  of  t  than  at  higher  values  of  t.  Since  the  energy  curve  is  ad- 
justed to  the  mean  of  the  observations,  there  will  be  a  tendency  toward 
plus  deviations  at  the  left  end  of  the  graphs,  and  a  less  marked 
tendency  toward  minus  deviations  at  the  right,  assuming  the  energy 

TABLE  A. — ILLUSTRATING  THE  NATURE  OF  THE  SELECTION  EFFECTED  IN 
ADVANCED  REGISTRY  BY  A  FIXED  FAT  ENTRANCE  REQUIREMENT 

(Note  increasing  increment  in  E  in  going  from  higher  to  lower  fat  percentages) 


t 

F 

M 

E 

Increment 
in  E 

000  omitted 

8.0 
7.0 
6.0 
5.0 
4.0 
3.0 
2.0 

360 
360 
360 
360 
360 
360 
360 

4  500 
5  143 
6  000 
7  200 
9  000 
12  000 
18  000 

2  381 
2  466 
2  579 
2  738 
2  976 
3  372 
4  164 

85 
113 
159 
238 
396 
792 

588 


BULLETIN  No.  245 


[June, 


curve  to  represent  the  true  relation  for  the  unselected  population. 
Bearing  this  in  mind,  we  may  now  consider  the  advanced  registry 
data  in  relation  to  the  hypothesis. 

Jersey  Register  of  Merit  Long-Time  Records. — The  data  for  this 
group  are  given  in  Tables  5  and  6,  and  Fig.  3.  Considering  the  graph, 
it  will  be  seen  that  the  energy  curve  does  not  conform  closely  to  the 
logarithmic  curve.  That  the  energy  curve  does  not  go  thru  the 
observations  quite  so  well  as  the  logarithmic  curve  is  shown  both  by 
inspection  and  by  the  errors.  The  logarithmic  curve,  of  course,  is 


4.4    4.9    4JB 


S.O    &»     9.4    SS     S»     t.O     At     8.4     9.9     9.6 

fAr  CONTC.NT  or  MILK 


7.0      7-t     7.4     79 


FIG.  3.  —  EELATION  BETWEEN  FAT  PERCENTAGE  AND  MILK  YIELD:    JERSEY 

REGISTER  OF  MERIT  LONG-TIME  RECORDS 

8,038  records.     Data  from  Table  6,  page  604.     (One  observation  at 
t  •=.  8.145.  M0  =:  4500  is  omitted  in  the  graph.) 

determined  solely  by  the  observations  on  the  selected  advanced  reg- 
istry population;  whereas  the  energy  curve  can  be  expected  to  con- 
form to  observations  only  on  a  random  sample  of  the  population.  In 
how  far  is  the  selection  effected  by  the  entrance  requirements  an  ex- 
planation of  the  difference  between  the  two  curves  (accepting  the 
logarithmic  curve  as  representing  the  observations)  ?  Without  at- 
tempting to  answer  quantitatively,  it  is  apparent  that  the  effect  of 
selection  would  be  to  produce  a  difference  similar  to  that  actually 
found.  Think  of  the  energy  curve  as  placed  slightly  lower  on  the 
graph  so  that  the  two  curves  coincide  at  the  right-hand  end.  Com- 
pare, now,  the  curved  wedge-shaped  surface  between  the  two,  with 
the  curved  wedge-shaped  surface  of  the  population  excluded  by  the 
entrance  requirements  as  illustrated  in  Fig.  A.  It  would  seem  quite 
possible  that  the  differential  selection  of  the  entrance  requirements 
is  entirely  responsible  for  the  deviations  of  the  logarithmic  curve, 
or  observations,  from  the  energy  curve. 


192S] 


RELATION  BETWEEN  FAT  CONTENT  AND  MILK  YIELD 


589 


Jersey  Register  of  Merit  Seven-Day  Records. — The  data  for  this 
group  are  given  in  Tables  7  and  8,  and  Fig.  4.  Judged  by  the  errors, 
the  energy  curve  fits  nearly  as  well  as  the  logarithmic  curve.  Visual 
impression  from  the  graph,  however,  is  favorable  to  the  logarithmic 
curve.  It  will  be  noted  that  the  difference  between  the  two  is  similar 
to  that  found  in  the  case  of  the  long-time  records. 


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far  CONTENT  of  MILK 

FIG.  4. — RELATION  BETWEEN  FAT  PERCENTAGE  AND  MILK  YIELD:   JERSEY 

REGISTER  OF  MERIT  SEVEN-DAY  RECORDS 
367  records.     Data  from  Table  8,  page  606 

Guernsey  Advanced  Register  Records. — The  data  for  this  group 
are  given  in  Table  9  and  Fig.  5.  The  relation  between  the  two  curves, 
as  shown  in  the  graph,  is  very  similar  to  that  noted  and  discussed  for 
the  Jersey  long-time  records. 


J«     Jfl     ¥.0     4t     +4    +.»    46     S.O     S.l     3.4     ft     5.8      «O     61     9.4     t.t     9»      7.0 


FIG.  5.  —  RELATION  BETWEEN  FAT  PERCENTAGE  AND  MILK  YIELD:    GUERNSEY 

ADVANCED  REGISTER  RECORDS 
3,564  records.     Data  from  Table  9,  page  607 

Ayrshire  Advanced  Registry  Records.  —  The  data  for  this  group 
are  given  in  Table  10  and  Fig.  6.  The  observations  show,  from  left 
to  right,  first  a  descending  tendency  and  then  an  ascending  tendency. 


590 


BULLETIN  No.  245 


[June, 


The  logarithmic  curve  is  not  fitted  to  the  whole  data  because  the  type 
used  is  not  adapted.  As  previously  pointed  out,  the  Ayrshire  entrance 
requirements  are  peculiar.  At  values  of  t  above  3.57-4.29,  selection 
becomes  more  severe,  and  consequently  the  mean  energy  yield  of  the 
right-hand  end  groups  is  increased.  Making  allowance  for  this,  the 
Ayrshire  data  differ  from  the  energy  curve  in  a  manner  similar  to 
that  for  the  Jersey  and  Guernsey,  and  in  accordance  with  expectation. 


Y/fLff  Of  MtLK-CWT. 

s_l_st_L_i_; 

6YRSH/KC 
aaactvent 

j.m. 
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113 

191 
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U      5* J-2      3.4     At     55 4*      4.2     **    4.6    44      &0      Si     £4     &* 

nir  COMTCMT  of  MILK 


FIG.  6. — RELATION  BETWEEN  FAT  PERCENTAGE  AND  MILK  YIELD:    AYRSHIRE 

ADVANCED  REGISTRY  RECORDS 
1,091  records.     Data  from  Table  10,  page  608 

Brown  Swiss  Register  of  Production  Records  (Age-Corrected). — 
The  data  for  this  group  are  given  in  Tables  11,  12  ,  and  13  and  Fig.  7. 
The  age-correction  factor  applied  here  is  that  for  the  Holstein  breed 
(for  lack  of  better  data)  and  may  be  subject  to  some  error.  The  graph 
shows  a  great  deal  of  irregularity  in  the  observations,  which  is  pos- 
sibly due  to  the  small  number  of  records,  311.  The  general  trend  of 
the  observations  is  in  conformity  with  the  energy  curve,  but  the  data 
are  hardly  satisfactory  for  the  purpose  of  fitting  a  curve. 


o  o  taaa  umo  HMf. 


^S> 


28     3.0     iJt     0*     9.9     J.fl     4.0    +t     +4    48     4.9     Sit 

ntr  COMTKHT  of  MILK 


FIG.  7.  —  RELATION  BETWEEN  FAT  PERCENTAGE  AND  MILK  YIELD:   BROWN 

Swiss  REGISTER  OF  PRODUCTION  RECORDS 
311  records,  age-corrected.     Data  from  Table  13,  page  611 


1923] 


RELATION  BETWEEN  FAT  CONTENT  AND  MILK  YIELD 


591 


Hoist ein-Friesian  Advanced  Register  Long-Time  Records. — The 
data  for  this  group  are  given  in  Tables  14,  15,  16,  and  17,  and  in 
Figs.  8  and  9.  Considering  Fig.  8,  which  is  based  on  Vols.  24  to  30, 
the  records  are  seen  to  be  exceptional.  The  center  of  the  group  shows 
some  tendency  to  conform  to  the  energy  curve.  But  the  right-hand 
portion  is  very  remarkable.  As  the  data  stand,  they  do  not  support 
the  hypothesis.*  That  the  conditions  of  official  testing  were  responsi- 


2* 

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200 
19* 

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9  Mt. 

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if     a   jo  A!  34  a.e  9.9    .&  +t   44  *e 

FXr  COKTCMT  Of  Mil* 


FIG.  8.  —  RELATION  BETWEEN  FAT  PERCENTAGE  AND  MILK  YIELD  :   HOLSTEIN- 

FRIESIAN  ADVANCED  REGISTER  LONG-TIME  RECORDS 
5,266  records,  1912-1919.    Data  from  Table  15,  page  613  (cf.  Figs.  1,  9,  10). 

ble  for  the  exceptional  results  shown  is  indicated  by  the  fact  that  Hoi- 
stein  cows,  under  the  conditions  of  the  cow  testing  association  (  Fig.  1  )  , 
showed  an  entirely  consistent  behavior  in  their  records.  Eckles7  has 
shown  experimentally  that  the  condition  of  the  cow  at  freshening 
materially  affects  milk  secretion,  qualitatively,  the  fat  percentage 
being  increased  by  a  fat  condition  of  the  cow.  It  is  commonly  be- 
lieved that  the  Holstein  cow  is  especially  susceptible  to  this  influence. 
It  may  be  offered  in  explanation  that  a  part  of  the  advanced  registry 


*It  may  be  noted  that  the  energy  basis  is,  nevertheless,  a  more  equitable 
basis  of  comparison  than  the  fat  basis,  as  shown  by  the  errors,  Table  23. 


592 


BULLETIN  No.  245 


Holstein  cows,  having  normally  a  somewhat  low  value  of  t  and  a  high 
value  of  M,  were  in  high  condition  at  freshening,  and  thereby  the 
value  of  t  was  greatly  increased  while  the  value  of  M  was  not  de- 
creased. Such  a  condition  might  distort  the  data  to  produce  the  effect 
observed. 

Because  of  the  exceptional  nature  of  the  above  records,  which  may 
be  called  "modern,"  the  earlier  records  of  Vols.  18  to  24  are  con- 
sidered. They  are  the  first  1,003  long-time  official  records  of  the 
breed.  The  data  (Fig.  9)  show  a  somewhat  similar  tendency,  but  in 
lesser  degree.  It  will  be  seen  that  judged  by  the  logarithmic  curve, 
the  energy  curve  does  not  fit  well;  but  judged  by  the  observations 
themselves,  it  fits  fairly  well.  This  view  is  supported  by  the  errors, 
which  are  not  much  greater  for  the  energy  curve  than  for  the 
logarithmic  curve. 


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A*      tf       it      30       42       ** 

Ktr  COMTEMT  Of  MILK 


FIG.  9. — RELATION  BETWEEN  FAT  PERCENTAGE  AND  MILK  YIELD:    HOLSTEIN- 

FRIESIAN  ADVANCED  REGISTER  LONG-TIME  RECORDS 
1,033  records,  1906-1913.    Data  from  Table  17,  page  615.     These  are 
the  first  1,003  long-time  official  records  of  the  breed.     Note  the  partial 
disappearance  of  the  discordantly  high  milk  yields  shown  at  the  higher 
fat  percentages  in  Fig.  8. 

Holstein-Friesian  AM.O.  Seven-Day  Records  (Age-Corrected). — 
The  data  for  this  group  are  given  in  Tables  18,  19,  and  20,  and  Fig.  10. 
The  records  represent  the  first  277  cows  admitted  (1894-1898)  to  the 
Holstein-Friesian  advanced  registry  under  the  system  of  official  tests. 
The  graph  shows  a  slight  tendency  of  the  data  in  the  direction  noted 
for  the  long-time  records.  While  there  is  not  the  closest  agreement 
between  the  energy  curve  and  the  logarithmic  curve,  yet  it  is  evident 
that  the  energy  curve  goes  thru  the  observations  strikingly  well.  Its 
mean  error  is  less  than  that  of  the  logarithmic  curve,  but  its  root  error 
is  somewhat  greater.* 


*It  should  be  noted  that  the  "modern"  seven-day  records  do  not  support  the 
hypothesis  at  all.  They  show,  in  fact,  a  tendency  to  constant  milk  yield.  Refer- 
ence is  had  to  those  seven-day  records  made  shortly  after  calving.  For  records 
made  some  time  after  calving,  the  energy  relation  may  hold.  The  seven-day  rec- 
ords are  being  studied  further  from  this  standpoint. 


1923] 


RELATION  BETWEEN  FAT  CONTENT  AND  MILK  YIELD 


593 


While  the  "modern"  Holstein  advanced  registry  records  do  not 
support  the  hypothesis,  the  early  records,  both  long-time  and  seven- 
day,  are  regarded  as  supporting  it  very  satisfactorily. 


sn 

540 


i.i    12    zs   a    i»    31 


VOLSTEIN  ,t.R.O. 

9asetnn»aM£. 


r-aiK 
/u. 


37     9.9     41     4*    4.S    4.7    +9 


FIG.  10. — RELATION  BETWEEN  FAT  PERCENTAGE  AND  MILK  YIELD:    HOLSTEIN- 

FRIESIAN  ADVANCED  REGISTER  SEVEN-DAY  RECORDS 
277  records,  1894-1898,  age-corrected.  Data  from  Table  20,  page  618. 
These  are  the  records  of  the  first  277  cows  of  the  breed  admitted  to  the 
advanced  register  under  the  present  system  of  official  supervision.  Note 
the  practically  complete  disappearance  of  the  discordantly  high  milk 
yields  at  the  higher  fat  percentages  shown  in  Fig.  8. 

Summary  of  Evidence. — The  coefficient  of  correlation  (Table  21) 
indicates  the  presence  of  a  definite  relation  between  percentage  fat 
content  and  yield  of  milk.  As  brought  out  further  by  the  mean 
milk  yields  and  by  the  fitted  curves  and  their  errors  (as  shown  in  the 
graphs  and  tables)  this  relation  is  in  excellent  conformity  with  that 
expressed  in  the  hypothesis  for  all  the  records  except  the  "modern" 
Holstein  advanced  registry  records. 

It  is  therefore  held  that  the  hypothesis  is  verified  by  the  evidence 
at  hand.* 


*The  hypothesis  of  this  paper  has  a  bearing,  on  the  problems  of  inheritance 
of  the  characters  fat  percentage  and  milk  yield.  The  low  value  of  r  as  found 
in  correlating  the  two  variables  has  given  rise  to  the  notion  that  the  genetic 
factors  responsible  for  the  two  characters  are  independently  transmitted  and 
capable  of  combination  in  any  way.  Such  may  be  the  fact.  But  we  must  re- 
member that  to  secure  the  simultaneous  development  of  high  fat  percentage  and 
high  milk  yield  would  involve  an  extraordinary  expenditure  of  energy.  The 
hypothesis  suggests  that  a  high  energy  yield  is  no  more  certain  of  attainment 
with  a  high  fat  percentage  than  with  a  low  fat  percentage;  and  that  there  is 
no  more  likelihood  of  securing  a  super-dairy  breed  by  crossing  a  high  fat  per- 
centage breed  with  a  high  milk  yielding  breed  than  there  is  within  either  breed 
itself,  so  far  as  the  direct  influence  of  the  genetic  factors  determining  the  two 
characters  in  question  is  concerned. 

An  alternative  explanation  of  the  relation  between  fat  percentage  and  milk 
yield  deserves  consideration.  If  the  mean  fat  percentage  of  the  various  milk 


594  BULLETIN  No.  245  [June, 

CORRECTION  OF  MILK  YIELD  FOR  FAT  CONTENT 

Derivation  of  Formula. — The  principal  product  of  the  dairy  cow 
is  her  mammary  product — milk, — variable  in  quantity  and  chemical 
composition.  Composition  itself,  as  measured  by  fat  percentage,  is  a 
factor  having  a  certain  definite  influence  on  quantity.  It  is  desirable 
to  express  the  mammary  product  in  terms  of  milk  of  some  certain 
standard  composition,  and  this  is  readily  possible  because  of  the  nature 
of  the  influence  of  composition  on  yield.  The  choice  of  the  standard 
composition  to  be  used  is  not  predetermined,  except  that  it  be  the 
normal  composition  of  milk  of  some  particular  fat  percentage.  For 
the  Holstein  breed  the  choice  might  be  the  mean  of  the  breed,  say 
milk  of  3.4  percent  fat;  for  the  Jersey  breed,  likewise,  5.4  percent 
fat.  For  general  convenience  and  utility,  it  is  better  to  have  a  single 
standard  for  all  cows,  and  normal  milk  of  4.0  percent  fat  has  been 
chosen  as  being  near  a  mean  and  most  convenient  of  use. 

The  problem  is  now  to  equate  the  milk  yield  at  varying  fat  per- 
centages to  the  standard  of  a  milk  having  a  fat  content  of  4.0  percent. 
The  equation  takes  the  form, 

Fat  corrected  yield  Enersv  vield 

of  milk  (pounds),  FCM    =  g      gy  %' -,    ,  ,  nr/ ^-- 

Energy  of  1  pound  of  4.0%  milk 

132.06  M  +  4964  F 


330.62 
=  .4  M  -f  15  F 

Application  of  Formula. — It  will  be  recalled  that  the  "modern" 
Holstein  advanced  registry  records  do  not  support  the  proposition  on 
which  this  formula  is  based.  There  may  be  some  doubt  as  to  whether 
the  formula  may  equitably  be  applied  to  this  class  of  records.  The 


yield  classes  be  determined,  it  is  found  that  there  is  a  decrease  in  fat  percent- 
age from  lower  to  higher  milk  yields.  'On  the  basis  of  this,  Gowen1  (p.  95) 
has  offered,  in  explanation  of  the  relation  between  fat  percentage  and  milk 
yield,  the  proposition  that  a  higher  milk  yield  requires  a  greater  expenditure 
of  energy  (in  total)  than  a  lower  milk  yield,  and  that  the  fat  or  fat  precursors 
of  the  milk  are  drawn  on  to  meet  this  energy  requirement,  thus  reducing,  to  some 
extent,  the  proportion  of  fat'  in  the  milk  at  the  higher  milk  yields.  According 
to  Gowen's  view,  milk  yield  is  cause  and  fat  percentage  is  effect  (milk  yield, 
however,  affecting  fat  percentage  only  to  a  minor  degree) ;  whereas,  according 
to  the  view  of  the  present  paper,  fat  percentage  (together  with  the  correlated 
solids-not-fat  percentage)  is  cause  and  milk  yield  is  effect  (fat  percentage  being, 
however,  only  one  of  many  factors  affecting  milk  yield).  Both  views  have  in 
common  the  recognition  of  an  energy  requirement  in  explanation  of  the  relation 
between  the  two  variables.  To  the  writers,  it  does  not  seem  reasonable  to  suppose 
that  the  fat  or  fat  precursors  of  the  milk  should  be  the  sole  source  of  the  energy 
required  in  milk  secretion:  whereas,  it  does  seem  reasonable  to  suppose  that  the 
energy  requirement  should  be  a  determining  factor  in  the  amount  of  milk 
secreted,  and  that  the  energy  requirement  should  be  in  proportion  to  the  energy 
content  of  the  solids  of  the  milk  secreted. 


M8S}  RELATION  BETWEEN  FAT  CONTENT  AND  MILK  YIELD  595 

only  apparent  reason  that  it  might  not  be  so  applied  would  be  that 
the  composition  of  the  milk  of  advanced  registry  Holstein  cows  (under 
the  particular  conditions  surrounding  the  production  of  their  records) 
is  different  from  that  of  other  cows  (or  Holstein  cows  under  ordinary 
conditions),  where  the  fat  percentage  is  the  same.  There  is  no  evi- 
dence that  it  is  different,  but  on  the  other  hand  there  is  some  evidence* 
that  it  is  not  different.  In  the  judgment  of  the  writers,  the  discordant 
results  noted  are  due  to  subjecting  part  of  the  population  to  unusual 
conditions  and  the  discord  would  disappear  if  the  whole  population 
were  subjected  to  the  same  condition.  The  formula  is  therefore  re- 
garded as  applicable  to  the  class  of  records  in  question. 

The  proposition  on  which  the  formula  is  based  is  supported  by  the 
use  of  mean  milk  yields  of  groups.  The  question  arises,  is  it  applicable 
to  individuals?  The  relation  E  =  132.06  M  -f-  4964  F  is  naturally 
subject  to  some  variation,  and  to  that  extent  there  is  the  probability 
of  error  in  applying  the  formula  to  the  individual.  That  such  error 
would  not  be  great  is  indicated  by  two  facts :  first,  the  fat  itself  rep- 
resents more  than  half  the  energy  of  the  milk  (except  when 
t  <  3.8)  ;  second,  the  solids-not-fat,  which  are  responsible  for  the 
remainder  of  the  energy,  are  closely  correlated  with  the  fat  (r  =  +.9). 
Hence,  the  formula  may  be  applied  to  the  individual  with  the  prob- 
ability of  only  slight  injustice.** 

The  recommendation  is  therefore  made  that  for  comparative  pur- 
poses in  considering  the  milk  production  of  cows,  the  yield  of  milk  be 
corrected  by  the  formula  .4  M  -|-  15  F ;  where  M  =  milk  yield,  in 
pounds,  and  F  =  fat  yield,  in  pounds.*** 


*  Unpublished  data,  Illinois  Agricultural  Experiment  Station. 

**It  would  be  more  accurate  to  determine  the  energy  value  calorimetrically. 
The  greater  accuracy  is  not  regarded  as  a  sufficient  offset  to  the  difficulties  in- 
volved in  the  calorimetric  determination  to  warrant  its  use,  ordinarily.  If  the 
energy  value  is  determined  directly  the  equation  would  take  the  form: 

E  C  M  =  — =  .3025  E 

330.62 

Where  both  the  solids  and  fat  are  determined,  the  equation  might  take  the 
form: 

F-S  C  M  =  4220  F  + 1860  S-N-F        ^^  p       «.  ^  g.N.p 
330.62 

***As  to  the  equity  of  this  correction,  further  evidence,  of  a  different 
sort,  is  to  be  had  from  the  feed  required  for  the  production  of  milk  of  different 
fat  percentages.  On  this,  a  great  deal  of  experimental  work  is  summarized  and 
generalized  in  the  feeding  standards  for  milk  production.  Table  B  analyzes 
several  standards  on  the  basis  of  the  energy  value  of  the  milk  solids.  It  will  be 
noted  from  the  table  that  the  feed  required  per  unit  energy  of  milk  is  practically 
a  constant  for  the  varying  fat  percentages  (except  with  the  Eckles  standard).  In 
point  of  feed  required,  the  evidence  of  the  feeding  standards  supports  the  equity 
of  the  correction  formula. 


596 


BULLETIN  No.  245 


[June, 


The  results  of  experimental  work  in  milk  production  are  generally 
stated  in  terms  of  milk  and  of  fat.  There  are  often  economic  condi- 
tions that  make  it  desirable  to  lay  stress  on  one  or  the  other  of  these 
terms.  In  other  cases,  where  a  physiological  comparison  is  desired, 
it  may  be  desirable  to  have  a  single  expression  to  cover  both  terms, 
and  for  such  purpose  the  above  formula  should  be  of  value.  To 
illustrate  specifically,  take  the  results  of  grading  up  from  scrub  cows 


TABLE  B. — RELATION  BETWEEN  PERCENTAGE  FAT  CONTENT  OP  MILK  AND  FEED 
REQUIRED  TER  UNIT  ENERGY  OF  THE  MILK  SOLIDS 

(The  table  shows  the  relative  values  of  the   feed  required  by  various  feeding 

standards  as  given  in  Larson  and  Putney,8  at  the  several  fat  percentages 

indicated.     Four-percent  miUc  is  taken  as  100  for  each  standard. 

The  energy  of  the  milk  solids  is  estimated  by  the 

formula  given  in  the  text.) 


Feeding 

Fat 

contem 

of  milk 

standard 

2.5% 

3.0% 

3.5% 

4.0% 

4.5% 

5.0% 

5.5% 

6.0% 

6.5% 

7.0% 

Haecker  

98 

99 

100 

101 

101 

101 

101 

102 

Savage  

95 

97 

99 

100 

101 

101 

101  , 

101 

101 

100 

Henry  and 

Morrison.  .  .  . 

96 

97 

99 

100 

101 

101 

101 

101 

101 

101 

Eckles  

102 

101 

100 

102 

104 

109 

115 

121 

Armsby  

91 

92 

96 

100 

100 

103 

103 

103 

105 

105 

We  may  now  develop  a  point  of  some  practical  interest,  namely,  the  relative 
feed  cost  of  producing  milk  as  affected  by  the  percentage  fat  content.  Table  B 
shows  the  nutrients  required  for  milk  production  (exclusive  of  maintenance)  at 
different  fat  percentages  to  be  in  proportion  to  the  energy  value  of  the  milk. 
We  have  seen  above  that  the  energy  yield  of  cows  is  constant,  so  far  as  it  is 
affected  by  the  fat  percentage  of  their  milk.  Therefore,  the  nutrients  required 
for  maintenance,  per  unit  energy  of  the  milk  produced,  are  a  constant  so  far  as 
they  are  affected  by  percentage  fat  content  (disregarding  any  correlation  between 
fat  percentage  and  size  of  cow).  It  follows,  then,  that  the  relative  feed  cost  of 
producing  milks  of  different  fat  percentages  is  substantially  in  accordance  with 
the  equation: 

Feed   cost   per  cwt.  milk   =   X  (.4  -(-  ,15t), 

where  X  is  the  feed  cost  per  cwt.  of  4.0-percent  milk.  To  illustrate,  if  the  feed 
cost  of  4.0-percent  milk  is  $2.00  per  cwt.,  then  the  corresponding  cost  of  3.0- 
percent  milk  is  $2.00  [.4  -j-  (.15)  (3)]  =$1.70;  and,  of  5.0-percent  milk,  $2.00 
[.4 -{-(.15)  (5)]  =$2. 30;  and  so  forth.  Or,  to  put  it  perhaps  more  simply, 
a  difference  of  1  in  the  percentage  fat  content  of  the  milk  corresponds  to  a  differ- 
ence in  feed  cost  which  is  equal  to  15  percent  of  the  feed  cost  of  4.0-percent  milk. 
It  is  plain,  at  this  point,  that  the  argument  of  this  paper  is  essentially  that 
the  energy  value  of  the  milk  solids  is  an  equitable  basis  of  comparison  of  the 
production  of  cows.  That  the  energy  value  should  be  expressed  in  terms  of  aver- 
age milk  of  4.0-percent  fat  content  is  purely  a  matter  of  convenience  and  desire 
to  retain  the  term  ' '  milk. ' '  It  was  stated  near  the  outset  that  the  relation 
between  fat  percentage  and  milk  yield  is  "simple  and  logical."  The  reason  for 
the  statement  is  seen  now,  since  the  laws  of  energetics  may  be  expected  to  be 
involved  in  the  secretion  of  milk,  as  they  are  in  other  life  activities.  Apparently, 
the  water  of  the  milk  represents  no  expenditure  of  energy  on  the  part  of  the 
mammary  gland.  The  osmotic  pressure  of  the  milk  and  the  blood  are  the  same, 
so  that  there  is  no  balance  of  osmotic  energy  with  which  to  reckon.  Consequently, 
the  energy  relation  goes  back  entirely  to  the  solids  of  the  milk. 


19SS] 


RELATION  BETWEEN  FAT  CONTENT  AND  MILK  YIELD 


597 


by  the  use  of  dairy  bred  bulls  as  reported  in  Bulletin  188  of  the  Iowa 
Agricultural  Experiment  Station.  The  daughters  of  the  Holstein 
bull  used  showed  a  milk  production  equal  to  190  percent  of  that  of 
the  dams,  and  a  fat  production  equal  to  159  percent.  The  average 
production  of  the  dams  was  3,894  pounds  FCM  and  of  the  daughters, 
6,602  pounds  FCM.  The  production  of  the  daughters,  on  this  basis, 
is  170  percent  of  that  of  the  dams;  and  we  may  say  that  the  dairy- 
bred  bull  has  increased  the  dairy  capacity  of  the  first  generation  by 
70  percent  when  compared  with  the  stock  with  which  he  was  mated 
(age  is  not  taken  into  account  here). 

The  formula  should  be  of  especial  value  in  comparing  the  pro- 
duction of  cows  having  a  considerable  difference  in  the  percentage 
fat  content  of  their  milk.  Table  C  has  been  prepared  from  the  pub- 
lished records  of  five  dairy  breeds  in  order  to  show  the  relation  be- 
tween the  highest  milk  and  highest  fat  records  in  each  breed.  Deci- 
mals are  omitted  from  the  milk  and  fat  records.*  Suppose  it  is  de- 
sired to  compare  the  records  of  the  first  two  cows  in  the  table.  Cow 
B.P.  has  a  recorded  fat  production  100  pounds  greater  than  cow 
S.P.P. ;  but  the  latter  has  more  milk  by  10,364  pounds.  Which  is  the 
better  record  ?  From  the  physiological  standpoint  of  work  performed, 
and  reduced  to  terms  of  4.0-percent  milk,  S.P.P.  has  the  better  record 
by  2,645  pounds.  In  like  manner,  comparison  may  be  made  between 
the  breeds,  if  desired. 

TABLE  C. — HIGHEST  MILK  AND  HIGHEST  FAT  RECORDS  OF  FIVE  BREEDS 

(August,  1922) 


Name  and  Number 

Milk 
Ibs. 

Fat 
Ibs. 

Fat 

% 

FCM* 
Ibs. 

FCM* 

relative 
values 

Segis  Pietertje  Prospect  HFHB  221846.  . 
Bella  Pontiac,  CHB  46321  

37  381 
27  017 

1   159 
1  259 

3.10 
4.66 

32  337 
29  692 

100 
92 

Murne  Cowen,  AGCC  195977  

24   (HIS 

1  098 

4.57 

26  073 

81 

Countess  Prue,  AGCC  43785  

18  627 

1    103 

5.92 

23  996 

74 

Garclaugh  May  Mischief,  ABA  27944..  . 
Lily  of  Willowmore,  ABA  22269  

25  329 
22  596 

895 
956 

3.53 
4.23 

23  557 
23  378 

73 

72 

Fauvic's  Star,  AJCC  313018  

20  616 

1  006 

4.88 

23  336 

72 

Lad's  Iota.  AJCC  350672  

18  632 

1  048 

5.63 

23   173 

72 

Hawthorn  Dairy  Maid,  BSBA  6753  

22  623 

927 

4.10 

22  954 

71 

*Milk  yield  corrected  for  fat  to  4.0-percent  fat. 


SUMMARY 


The  relation  between  percentage  fat  content  and  yield  of  milk  is 
shown  by  analysis  of  ten  groups  of  cow  records,  comprizing  23,302 
records  in  all.  Accordant  results  are  shown  by  nine  groups: 


*The  writers  feel  that  the  extensive  printing  of  meaningless  decimals  in 
data  of  this  nature  as  practiced  by  Agricultural  Experiment  Stations  and  Breed 
Associations,  is  without  justification. 


598  BULLETIN  No.  245  [June, 

970  Jersey  Cow  Testing  Association  yearly  records 

8,038  Jersey  Register  of  Merit  long-time  records 

367  Jersey  Register  of  Merit  seven-day  records 

3,564  Guernsey  Advanced  Register  long-time  records 

1,091  Ayrshire  Advanced  Registry  long-time  records 

311  Brown-Swiss  Register  of  Production  long-time  records 

2,773  Holstein  Cow  Testing  Association  yearly  records 

277  Holstein-Friesian  Advanced  Register  seven-day  records  (Vols.  1-9) 

1,003  Holstein-Friesian  Advanced  Register  long-time  records  (Vols.  18-24) 

Discordant  results  are  shown  by  one  group  : 
5,266  Holstein-Friesian  Advanced  Register  long-time  records  (Vols.  24-30) 

The  relation  supported  by  the  majority  of  the  data  is  made  the 
basis  of  a  correction  formula  for  milk  yield  designed  to  equate  for  the 
influence  of  fat  percentage  on  yield. 

CONCLUSIONS 

The  percentage  fat  content  of  the  milk  is  a  factor  affecting  milk 
yield.  So  far  as  affected  by  fat  percentage,  the  milk  yield  is  inversely 
proportional  to  the  energy  value  of  the  milk  solids  per  unit  of  milk; 
that  is,  the  energy  value  of  the  milk  solids,  in  the  total  milk  yield, 
is  a  constant.  For  a  group  of  comparable  cows,  the  relation  be- 
tween fat  percentage  and  milk  yield  is  expressed  by  the  equation 

o 

M  —  —  —  —  —  —  ;  where  M  is  the  average  milk  yield  (in  pounds),  t  is 

fat  percentage,  and  a  is  a  constant  determined  in  value  by  the  pro- 
ductive level  of  the  particular  group.     As  corollaries  :    F  =  .Ola  — 
.0266a  ,  .06036a  .03376a 


2156+T' 
where  F  is  fat,  S-N-F  is  solids-not-fat,  S  is  solids  (all,  in  pounds) 

and  a  is  the  same  constant  as  above. 

The  milk  yields  of  cows  may  be  corrected  for  the  influence  of  fat 
content  to  the  physiological  equivalent  of  4.0-percent  (fat)  milk  by 
the  equation,  F  C  M  =  .4M  -f  15F  ;  where  F  C  M  is  "fat  corrected 
milk,"  M  is  the  actual  milk  yield,  and  F  is  the  actual  fat  yield  (all, 
in  pounds). 

LITERATURE  CITED 

1.  GOWEN,  JOHN  W.     Report  of  Progress  on  Animal  Husbandry  Investiga- 
tions in  1919.     Maine  Agr.  Exp.  Sta.  Bui.  283.     1919. 

2.  GOWEN,   JOHN   W.     Variations   and   Mode   of   Secretion   of   Milk  Solids. 
Jour.  Agr.  Research,  16,  3,  79-102.     1919. 

3.  STOCKING,  W.  A.,  AND  BREW,  J.  D.     Milk  —  The  Essential  Food.     The 
Dairymen's  League  News,  Jan.  10,  1920. 

4.  OVERMAN,  O.  R.     Food  Values  and  Dairy  Products.     111.  Agr.  Exp.  Sta. 
Circ.  235.     1919. 

5.  MINER,  JOHN  RICE.     Fitting  Logarithmic  Curves  by  the  Method  of  Mo- 
ments.    Jour.  Agr.  Research,  3,  5,  411.     1915. 

6.  ROBERTS,  ELMER.     Correlation  Between  the  Percentage  of  Fat  in  Cow's 
Milk  and  the  Yield.     Jour.  Agr.  Research,  14,  2,  67.     1918. 

7.  ECKLES,  C.  H.     Influence  of  Fatness  of  Cow  at  Parturition  on  Percent 
of  Fat  in  the  Milk.     Mo.  Agr.  Exp.  Sta.  Bui.  100.     1912. 

8.  LARSON,  C.  W.,  AND  PUTNEY,  F.  S.     Dairy  Cattle  Feeding  and  Manage- 
ment.    1917. 


19SS} 


RELATION  BETWEEN  FAT  CONTENT  AND  MILK  YIELD 


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BULLETIN  No.  245 


TABLE  2. — COMPARISON  OP  MEAN  MILK  YIELDS  AS  OBSERVED,  AND  AS  CALCU- 
LATED FROM  FITTED  LOGARITHMIC  AND  CONSTANT  ENERGY  CURVES 

Grade  and  Pure-Bred  Holstein  Cow  Testing  Association  Records 
(See  Table  1) 


t 

f 

M0 

M, 

D 

Me 

D 

2.545 

3 

8  500 

8  483 

+     17 

8  366 

+   134 

2.645 

10 

7  400 

8  276 

-   876 

8  209 

-   809 

2.745 

17 

8  147 

8  089 

+     58 

8  057 

+     90 

2.845 

36 

7  778 

7  919 

-    141 

,      7  910 

-   132 

2.945 

86 

8  023 

7  761 

+  262 

7  769 

+  254 

3.045 

139 

7  608 

7  615 

-       7 

7  633 

-     25 

3.145 

202 

7  718 

7  478 

+   240 

7  502 

+  216 

3.245 

238 

7  277 

7  348 

-     71 

7  375 

-     98 

3.345 

337 

7  384 

7  225 

+   159 

7  252 

+  132 

3.445 

322 

7  220 

7  107 

+   113 

7  133 

+     87 

3.545 

283 

7  058 

6  994 

+     64 

7  018 

+     40 

3.645 

256 

6  871 

6  886 

-      15 

6  907 

-     36 

3.745 

218 

6  610 

6  781 

-    171 

6  799 

-   189 

3.845 

169 

6  808 

6  680 

+   128 

6  695 

+   113 

3.945 

140 

6  529 

6  582 

-     53 

6  593 

-     64 

4.045 

99 

6  389 

6  487 

-     98 

6  495 

-    106 

4.145 

65 

6  654 

6  394 

+   260 

6  399 

+  255 

4.245 

47 

6  117 

6  304 

-    187 

6  307 

-    190 

4.345 

36 

6  194 

6  216 

-     22 

6  217 

-     23 

4.445 

20 

6  100 

6  130 

-      30 

6  129 

-     29 

4.545 

16 

5  438 

6  045 

-   607 

6  044 

-   606 

4.645 

14 

5  929 

5  963 

-     34 

5  961 

-     32 

4.745 

7 

5  929 

5  882 

+     47 

5  881 

+     48 

4.845 

5 

4  900 

5  802 

-  902 

5  802 

-  902 

4.945 

4 

6  750 

5  724 

+  1026 

5  726 

+  1024 

5.045 

1 

6  500 

5  647 

+  853 

5  652 

+  848 

5.245 

1 

5  500* 

5.445 

2 

6  500* 

Mean  error  

248 

249 

Root  mean-square  error  

397 

391 

*Excluded  in  fitting  curves  and  computing  errors. 


1923] 


RELATION  BETWEEN  FAT  CONTENT  AND  MILK  YIELD 


601 


TABLE  3. — CORRELATION  OF  THE  VARIABLES  PERCENTAGE  FAT  CONTENT 
AND  YIELD  OF  MILK 

Data  from  Jersey  (Grade  and  Pure-Bred)  Cow  Testing  Association  Yearly  Records 

Percentage  fat  content  of  milk;  class  mid-points  (add   .045) 


3.6 

3  7 

3  8 

s  q 

4  0 

4   1 

4  ?, 

4  3 

4  4 

4  5 

4  6 

4.7 

4  8 

4  q 

5  0 

5  1 

5  ?, 

^ 

25 

1 

1 

1 

J2 

35 

1 

1 

4 

4 

2 

2 

7 

7 

7 

7 

1? 

13 

11 

J2 

45 

2 

3 

3 

3 

6 

q 

q 

13 

13 

13 

15 

16 

17 

•O 

55 

2 

i 

4 

5 

8 

10 

?3 

13 

20 

20 

?q 

17 

17 

14 

CD 

65 
75 

I 

3 
1 

3 

2 

a 

4 

2 
?, 

9 
6 

8 
4 

12 

8 

12 
6 

7 
4 

13 
11 

11 

7 

17 

7 

6 
1 

9 
3 

g 

85 

1 

1 

1 

1 

2 

3 

2 

1 

2 

o 

95 

1 

2 

1 

1 

U 

Total 

2 

1 

7 

7 

12 

16 

20 

35 

46 

46 

59 

54 

66 

69 

71 

54 

55 

Yield  of  milk  (cwt.); 
class  mid-points 

5.3 

5.4 

5.5 

2 
3 
17 
18 
8 
3 
2 
1 

5.6 

3 
6 
8 
16 
5 
2 

5.7 

5.8 

5.9 

6.0 

1 
4 
9 

2 

1 

6.1 

6.2 

6.3 

6.4 

6.5 

6.6 

6.7 

6.8 

Total 

25 
35 
45 
55 
65 
75 
85 
95 

2 
6 
8 
6 

7 

I 

8 
9 
10 
11 

1 
7 
3 
9 
1 

13 
141 
226 
311 
177 
74 
21 
7 

12 
14 
18 

7 
3 
2 

14 
14 
24 
14 
2 
2 

2 
1 

1 

1 
3 

2 

3 
1 

1 

2 

1 
1 

1 

1 

1 

1 

1 

40 

29 

21 

17 

3 

Total 

56 

70 

54 

41 

6 

4 

2 

2 

2 

2 

1 

970 

602 


BULLETIN  No.  245 


[June, 


TABLE  4. — COMPARISON  OF  MEAN  MILK  YIELDS  AS  OBSERVED,  AND  AS  CALCU- 
LATED FROM  FITTED  LOGARITHMIC  AND  CONSTANT  ENERGY  CURVES 

Grade  and  Pure-Bred  Jersey  Cow  Testing  Association  Records 
(See  Table  3) 


t 

f 

M0 

M, 

D 

Me 

D 

3.645 

2 

4  541* 

3.745 

1 

6  515 

6  554 

-   39 

6  469 

+  46 

3.845 

7 

6  785 

6  385 

+  400 

6  369 

+  416 

3.945 

7 

6  928 

6  249 

+  679 

6  273 

+  655 

4  .  045 

12 

5  583 

6  133 

-  550 

6  179 

-  596 

4.145 

16 

6  124 

6  030 

+  94 

6  088 

+  36 

4.245 

20 

5  400 

5  937 

-  537 

6  000 

-  600 

4.345 

35 

5  700 

5  851 

-  151 

5  915 

-  215 

4.445 

46 

5  565 

5  770 

-  205 

5  832 

-  267 

4.545 

46 

5  980 

5  694 

+  286 

5  750 

+  230 

4.645 

59 

5  568 

5  621 

-  53 

5  672 

-  104 

4  .  745 

54 

5  444 

5  552 

-  108 

5  595 

-  151 

4.845 

66 

5  712 

5  485 

+  227 

5  520 

+  192 

4.945 

69 

5  572 

5  420 

+  152 

5  448 

+  124 

5.045 

71 

5  430 

5  356 

+  74 

5  377 

+  53 

5.145 

54 

4  815 

5  295 

-  480 

5  308 

-  493 

5.245 

55 

4  827 

5  235 

-  408 

5  241 

-  414 

5.345 

56 

5  160 

5  176 

-   16 

5  176 

-   16 

5.445 

70 

5  243 

5  119 

+  124 

5  112 

+  131 

5.545 

54 

5  407 

5  062 

+  345 

5  050 

+  357 

5.645 

40 

5  000 

5  007 

-7 

4  989 

+   11 

5.745 

29 

4  845 

4  952 

-  107 

4  930 

-  85 

5.845 

41 

5  256 

4  898 

+  358 

4  872 

+  384 

5.945 

21 

4  595 

4  845 

-  250 

4  815 

-  220 

6.045 

17 

4  382 

4  792 

-  410 

4  760 

-  378 

6.145 

3 

4  088 

4  740 

-  652 

4  705 

-  617 

6.245 

6 

5  666 

4  689 

+  977 

4  653 

+  1013 

6.345 

4 

4  779 

4  638 

+  141 

4  601 

+  178 

6.445 

2 

5  495 

4  588 

+  907 

4  550 

+  945 

6.545 

2 

4  735 

4  538 

+  197 

4  501 

+  234 

6.645 

2 

4  281 

4  488 

-  207 

4  453 

-  172 

6.745 

2 

4  670 

4  439 

+  231 

4  405 

+  265 

6.845 

1 

3  417 

4  390 

-  973 

4  359 

-  942 

Mean  error  

323 

329 

Root  mean-square  error  

421 

428 

*Excluded  in  fitting  curves  and  computing  errors. 


19  US] 


RELATION  BETWEEN  FAT  CONTENT  AND  MILK  YIELD 


603 


TABLE  5. — CORRELATION  OP  THE  VARIABLES  PERCENTAGE   FAT  CONTENT  AND 

YIELD  OP  MILK 

Data  from  Jersey  Register  of  Mprii,  Vols.  1916,  1917,  1918,  1919 
All  Long-Time  Records,  Including  Reentries 

Percentage  fat  content  of  milk;  class  mid-points  (add   .045) 


3  8 

A  9 

4  0 

1  1 

4  2 

4  8 

4  4 

1  ri 

4  6 

4  7 

4  R 

1  't 

r>  0 

5  1 

fi  •> 

5  3 

5  4 

5  5 

5  6 

~i  1 

ft  8 

S  9 

Continued  below 

35 
45 
55 
65 
75 
85 
95 
105 
115 
125 
135 
145 
155 
165 
175 
185 
195 

1 

42 
70 
112 
92 
09 
45 
21 
12 
10 
6 
.1 

2 
61 
80 
153 
110 
55 
32 
25 
17 
8 
5 
1 
1 

5 

«8 
92 
159 
97 
48 
88 
21 
11 
8 
2 
2 
3 
1 

7 
79 
97 
134 
100 
56 
31 
22 
13 
5 
4 
3 

12 
09 
130 
156 
90 
56 
30 
24 
12 
4 
4 

fll 

14 
62 
141 
109 
92 
5t 
33 
15 
15 
2 
8 
1 

20 
80 
121 
108 
84 
47 
30 
13 
6 
5 
3 
2 

22 
62 
119 
81 
68 
43 
25 
28 
5 
7 
2 
1 
\ 

20 
63 
125 
80 
46 
41 
28 
9 
5 
2 
1 
1 

24 

74 
94 
73 
41 
33 
20 
6 
.7 
2 
2 
2 

1 

2 
15 
20 
22 
14 
10 
6 
1 
1 

1 

18 
18 
32 
20 
12 
11 
11 
2 
8 
2 

8 
19 
38 
38 
29 
22 
13 

6 
6 
2 

8 

8 
37 
88 
52 
33 
20 
20 
13 
7 
8 

Hi 
40 
61 
70 
44 
31 
14 
4 
4 
3 
1 
2 
1 

25 

65 
107 
95 
59 
40 
22 
13 
11 
5 
2 

24 
01 
102 
74 
51 
43 
19 
16 
9 
5 
8 

2 
1 
2 
8 
1 
1 

2 
2 
8 
7 
5 
8 
2 

4 
1 
7 
9 
2 
7 

1 

"i 
1 

1 

1 

1 

1 

1 
1 

2 

1 

ft 

1 

1 

1 

Total 

1 

2 

11 

.SO 

85 

92 

125 

178 

233 

291 

445 

407 

483 

550 

555 

551 

596 

541 

519 

404 

421 

378 

6.0 

6.1 

6.2 

8.3 

6.4 

6.5 

6.6 

6.7 

6.8 

6.9 

7.0 

7.1 

7.2 

7.8 

7.4 

7.5 

7.6 

7.7 

7.8 

7.9 

8.0 

8.1 

Total 

35 
45 
55 
65 
75 
85 
95 
105 
115 
125 
135 
145 
155 
165 
175 
185 
195 

1 

1 
251 
988 
1593 
1735 
1348 
853 
542 
330 
187 
100 
59 
28 
14 
7 
1 
1 

18 

54 
66 
66 
41 
22 
17 

a 

6 

a 

i 

2 

27 
42 
55 
45 
27 
15 
10 
3 
2 
1 

10 
49 
37 
24 
20 
15 
8 
1 

15 
26 

30 
18 
19 
4 
5 
4 

14 
28 
27 
14 
7 
5 
2 
2 
2 

14 
14 
20 
13 

a 

6 

11 
12 
16 

4 

4 
5 
10 
9 
7 

4 
4 
5 

3 

2 
6 

B 

"6 
1 

1 
2 
1 
1 

1 
1 

1 

1 

1 

4 

1 

a 

8 

1 

1 

2 
8 

2 

1 
1 

1 
1 

1 

1 

1 

1 

1 

1 

1 

Total 

304 

228 

160 

121 

102 

75 

47 

33 

16 

21 

9 

7 

3 

0 

1 

2 

0 

0 

0 

0 

0 

l 

8038 

604 


BULLETIN  No.  245 


[June, 


TABLE  6. — COMPARISON  OP  MEAN  MILK  YIELDS  AS  OBSERVED,  AND  AS  CALCU- 
LATED FROM  LOGARITHMIC  AND  CONSTANT  ENERGY  CURVES 

Jersey  Register  of  Merit,  Vols.  1916,  1917,  1918,  1919 
All  Long-Time  Records,  Including  Reentries 

(See  Table  5) 


t 

f 

Mo 

M, 

D 

Me 

D 

3.845 

1 

9  500 

10  415 

-   915 

9  940 

-   440 

3.945 

2 

11  000 

10  146 

+   854 

9  789 

+  1211 

4.045 

11 

9  227 

9  913 

-    686 

9  643 

-   416 

4.145 

30 

9  700 

9  707 

-        7 

9  502 

+    198 

4.245 

35 

10  357 

9  520 

+  837 

9  364 

+  993 

4.345 

92 

9  572 

9  349 

+   223 

9  231 

+   341 

4.445 

125 

9  384 

9   190 

+    194 

9   101 

+  283 

4.545 

178 

9  061 

9  041 

+     20      -. 

8  974 

+     87 

4.645 

233 

8  954 

8  900 

+     54 

8  851 

+    103 

4.745 

291 

8  654 

8  766 

-    112 

8  732 

-     78 

4.845 

445 

8  606 

8  639 

-     33 

8  615 

-       9 

4.945 

407 

8  643 

8  516 

+    127 

8  502 

+    141 

5.045 

483 

8  497 

8  399 

+     98 

8  392 

+    105 

5.145 

550 

8  214 

8  285 

-     71 

8  284 

-      70 

5.245 

555 

8  073 

8  175 

-    102 

8  179 

-   106 

5.345 

551 

7  979 

8  068 

-     89 

8  077 

-     98 

5.445 

596 

7  885 

7  964 

-     79 

7  978 

-     93 

5.545 

541 

7  810 

7  862 

-     52 

7  881 

-     71 

5.645 

519 

7  646 

7  763 

-   117 

7  786 

-   140 

5.745 

464 

7  801 

7  666 

+   135 

7  693 

+    108 

5.845 

421 

7  255 

7  572 

-   317 

7  603 

-   348 

5.945 

378 

7  378 

7  478 

-    100 

7  514 

-    136 

6.045 

304 

7  535 

7  387 

+   148 

7  428 

+   107 

6.145 

228 

7  078 

7  297 

-   219 

7  343 

-   265 

6.245 

160 

6  907 

7  209 

-    302 

7  261 

-    354 

6.345 

121 

6  929 

7  122 

-    193 

7  180 

-   251 

6.445 

102 

6  746 

7  036 

-   290 

7   102 

-   356 

6.545 

75 

6  807 

6  951 

-    144 

7  025 

-    218 

6.645 

47 

6  308 

6  869 

-   561 

6  949 

-    641 

6.745 

33 

7  075 

6  786 

+   289 

6  875 

+   200 

6.845 

16 

6  306 

6  704 

-    398 

6  803 

-   497 

6.945 

21 

7  452 

6  624 

+  828 

6  732 

+   720 

7.045 

9 

7  056 

6  544 

+  512 

6  662 

+   394 

7.145 

7 

7  500 

6  466 

+  1034 

6  595 

+   905 

7.245 

3 

6  166 

6  387 

-    221 

6  528 

-    362 

7.345 

1* 

9  250 

6  310 

+  2940 

6  463 

+2787 

7.445 

1 

3  500 

6  234 

-2734 

6  399 

-2899 

7.545 

2 

5  500 

6  158 

-   658 

6  336 

-  836 

8.145 

1 

4  500** 

Mean  error  

439 

457 

Root  mean-square  error  

770 

777 

*Taken  from  Roberts,6  Table  V. 

**Excluded  in  fitting  curves  and  computing  errors. 


19183] 


RELATION  BETWEEN  FAT  CONTENT  AND  MILK  YIELD 


605 


TABLE  7. — CORRELATION  OF  THE  VARIABLES  PERCENTAGE  FAT  CONTENT  AND 

YIELD  OF  MILK 

Data  from  Jersey  Register  of  Merit,  Vols.  1911,  1913,  1915,  1916,  1917,  1918,  1919 
All  Seven-Day  Records  of  Cows  Four  Years  Old  and  Over 

Percentage  fat  content  of  milk;  class  mid-points  (add   .045) 


3.G 

3.7 

3.8 

3.9 

4.0 

4.1 

4.2 

4.3 

4.4 

4.5 

4.6 

4.7 

4.8 

4.9 

5.0 

5.1 

8.2 

5.8 

5.4 

5.5 

6.6 

5.7 

Continued  below 

190 
210 
230 
250 
270 
290 
310 
330 
350 
370 
390 
410 
430 
450 

1 
1 

"2 
1 

8 
2 

2 
8 
1 

1 
8 
1 
2 

3 

6 
4 
4 
2 
1 
1 
1 

8 

4 
4 

4 

6 
4 
5 
3 
3 

ti 
3 
2 
2 

3 
14 
3 
3 
1 
3 
1 
2 

4 
10 
7 
1 

"i 
i 
i 

8 
3 
5 
1 

3 

6 
5 
2 
4 
<3 
4 

1 
7 
2 

3 
2 
9 

4 
1 
1 

(i 
11 

"3 
3 
3 

5 

2 

a 

3 

3 
] 

1 
4 

8 

1 

1 

8 

2 

1 

2 

2 

1 

1 

3 

2 

1 
I 

1 

1 

1 

1 
1 

1 

1 

•1 

1 

1 

1 

1 

2 

1 

l 

1 

1 

1 

1 

Total 

1 

4 

1 

6 

c. 

5 

13 

(i 

15 

20 

27 

30 

25 

1(5 

24 

22 

24 

23 

17 

7 

12 

9 

5  8 

5  q 

R  0 

R  1 

R  ? 

6.3 

R  4 

R  5 

R  R 

R  7 

6  8 

R  <) 

7  0 

7   1 

7   V 

7  8 

7  4 

7   5 

7  R 

7  7 

7   X 

Total 

190 

1 

1 

2 

210 

8 

A 

1 

1 

1 

1 

1 

1 

1 

1 

22 

230 

4 

4 

8 

1 

1 

1 

43 

250 

1 

fl 

1 

1 

41 

270 

1 

1 

1 

•1 

1 

1 

1 

71 

290 

2 

62 

310 

1 

35 

330 

2 

1 

32 

350 

25 

370 

1 

14 

390 

7 

410 

6 

430 

1 

2 

450 

1 

5 

Total 

9 

14 

0 

e 

5 

2 

5 

1 

0 

1 

0 

2 

1 

0 

0 

1 

0 

0 

0 

0 

1 

367 

606 


BULLETIN  No.  245 


[June, 


TABLE  8. — COMPARISON  OF  MEAN  MILK  YIELDS  AS  OBSERVED.  AND  AS  CALCU- 
LATED FROM  LOGARITHMIC  AND  CONSTANT  ENERGY  CURVES 

Jersey  Register  of  Merit,  Vols.  1911,  1913,  1915,  1916,  1917,  1918,  1919 
All  Seven-Day  Records  of  Cows  Four  Years  and  More  of  Age 

(See  Table  7) 


t 

f 

Mo 

M, 

D 

Me 

D 

3.645 

1 

350.0 

362.7 

-12.7 

353.2 

-   3.2 

3.745 

4 

360.0 

354.4 

+   5.6 

347.7 

+  12.3 

3.845 

1 

330.0 

347.1 

-17.1 

342.3 

-12.3 

3.945 

6 

353.3 

340.5 

+  12.8 

337.2 

+  16.1 

4.045 

6 

333.3 

334  5 

-   1.2 

332.1 

+   1.2 

4.145 

5 

338.0 

328.9 

+  9.1 

327.2 

+  10.8 

4.245 

13 

325.4 

323.6 

+   1.8 

322.5 

+  2.9 

4.345 

6 

336.7 

318.7 

+  18.0 

317.9 

+  18.8 

4.445 

15 

319.3 

313.9 

+   5.4 

313.4 

+  5.9 

4.545 

20 

311.0 

309.4 

+   1.6 

309.1 

+   1.9 

4.645 

27 

311.5 

305.1 

+   6.4 

304.8 

+  6.7 

4.745 

30 

295.3 

301.0 

-   5.7 

300.7 

-   5.4 

4.845 

25 

286.0 

297.0 

-11.0 

296.7 

-10.7 

4.945 

16 

295.0 

293.1 

+    1.9 

292.8 

+   2.2 

5.045 

24 

295.8 

289.3 

+   6.5 

289.0 

+   6.8 

5.145 

22 

277.3 

285.7 

-   8.4 

285.3 

-   8.0 

5.245 

24 

271.7 

282.1 

-10.4 

281.7 

-10.0 

5.345 

23 

273.5 

278.6 

-    5.1 

278.2 

-   4.7 

5.445 

17 

271.2 

275.2 

-   4.0 

274.8 

-   3.6 

5.545 

7 

284.3 

271.9 

+  12.4 

271.4 

+  12.9 

5.645 

12 

261.7 

268.6 

-   6.9 

268.1 

-   6.4 

5.745 

9 

267.8 

265.4 

+   2.4 

265.0 

+   2.8 

5.845 

9 

243.3 

262.2 

-18.9 

261.8 

-18.5 

5.945 

14 

255.7 

259.1 

-   3.4 

258.8 

-   3.1 

6.045 

6 

246.7 

256.1 

-  9.4 

255.8 

-   9.1 

6.145 

6 

273.3 

253.1 

+20.2 

252.9 

+  20.4 

6.245 

5 

270.0 

250.1 

+  19.9 

250.1 

+  19.9 

6.345 

2 

260.0 

247.2 

+  12.8 

247.3 

+  12.7 

6.445 

5 

230.0 

244.3 

-14.3 

244.6 

-14.6 

6.545 

1 

270.0 

241.4 

+  28.6 

241.9 

+  28.1 

6.745 

1 

210.0 

235.9 

-25.9 

236.8 

-26.8 

6.945 

2 

200.0 

230.3 

-30.3 

231.8 

-31.8 

7.045 

1 

230.0 

.     227.6 

+   2.4 

229.5 

+      .5 

7.345 

1 

210.0 

219.6 

-  9.6 

222.6 

-12.6 

7.845 

1 

210.0 

206.7 

+  3.3 

212.0 

-   2.0 

Mean  error  

10.4 

10.4 

Root  mean-square  error  

13.0 

13.1 

RELATION  BETWEEN  FAT  CONTENT  AND  MILK  YIELD 


607 


TABLE  9. — COMPARISON  OF  MEAN  MILK*  YIELDS  AS  OBSERVED.  AND  AS  CALCU- 
LATED FROM  LOGARITHMIC  AND  CONSTANT  ENERGY  CURVES 

Guernsey  Advanced  Register* 
All  Entries  and  Reentries  to  and  Including  Vol.  XXIX 


t 

f 

M0 

M, 

D 

Me 

D 

3.7 

4 

10  750 

10  992 

-  242 

10  393 

+  357 

3.8 

4 

10  749 

10  718 

+  31 

10  232 

+  517 

3.9 

8 

10  000 

10  456 

-  456 

10  076 

-  76 

4.0 

16 

10  563 

10  216 

+  346 

9  925 

+  637 

4.1 

41 

9  908 

9  995 

-  87 

9  778 

+  130 

4.2 

68 

9  661 

9  790 

-  129 

9  635 

+  26 

4.3 

111 

9  484 

9  599 

-  115 

9  497 

-  13 

4.4 

122 

9  782 

9  421 

+  361 

9  362 

+  420 

4.5 

187 

9  346 

9  253 

+  93 

9  232 

+  114 

4.6 

211 

9  359 

9  095 

+  264 

9  105 

+  254 

4.7 

246 

8  912 

8  945 

-  33 

8  981 

-   «9 

4.8 

275 

8  949 

8  804 

+  145 

8  861 

+  88 

4.9 

275 

8  824 

8  670 

+  154 

8  744 

+  80 

5.0 

294 

8  644 

8  542 

+  102 

8  629 

+  15 

5.1 

305 

8  436 

8  420 

+   16 

8  518 

-  82 

5.2 

273 

8  367 

8  303 

+  64 

8  410 

-  43 

5.3 

241 

8  279 

8  191 

+  88 

8  304 

-  25 

5.4 

216 

8  166 

8  083 

+  83 

8  201 

-  35 

5.5 

204 

8  151 

7  980 

+  171 

8  101 

+  50 

5.6 

135 

7  909 

7  881 

+  28 

8  003 

-  94 

5.7 

87 

7  951 

7  785 

+  166 

7  907 

+  44 

5.8 

76 

7  552 

7  693 

-  141 

7  813 

-  261 

5.9 

52 

7  750 

7  604 

+  146 

7  722 

+  28 

6.0 

42 

7  083 

7  518 

-  435 

7  633 

-  550 

6.1 

21 

7  297 

7  435 

-  138 

7  546 

-  249 

6.2 

20 

6  599 

7  354 

-  755 

7  461 

-  862 

6.3 

10 

6  950 

7  276 

-  326 

7  377 

-  427 

6.4 

7 

7  964 

7  199 

+  765 

7  296 

+  668 

6.5 

7 

6  678 

7  111 

-  433 

7  216 

-  538 

6.6 

3 

6  249 

7  055 

-  806 

7  138 

-  889 

6.7 

1 

6  250 

6  985 

-  735 

7  062 

-  812 

6.8 

1 

6  249 

6  917 

-  668 

6  987 

-  738 

6.9 

1 

9  250 

6  852 

+  2398 

6  914 

+2336 

Mean  error  

331 

349 

Root  mean-square  error  

546 

569 

*From  Roberts,'  Table  X. 


608 


BULLETIN  No.  245 


[June, 


TABLE  10. — COMPARISON  OF  MEAN  MILK  YIELDS  AS  OBSERVED,  AND  AS  CALCU- 
LATED FROM  LOGARITHMIC  AND  CONSTANT  ENERGY  CURVES 

Ayrshire  Advanced  Registry  (Ayrshire  Breeders'  Association  Year  Book),   1907, 

1911,  1913,  1914* 


t 

f 

M0 

M, 

D 

Me 

D 

3.0 

1 

12  000 

11  581 

+  419 

:    11  012 

+  988 

3.1 

2 

11  000 

11  063 

-  63 

10  820 

+  180 

3.2 

5 

10  400 

10  683 

-  283 

10  636 

-  236 

3.3 

14 

10  536 

10  385 

+  151 

10  457 

+  79 

3.4 

49 

10  082 

10  142 

-  60 

10  285 

-  203 

3.5 

56 

9  768 

9  938 

-  170 

10  118 

-  350 

3.6 

75 

9  720 

9  763 

-  43 

9  956 

-  236 

3.7 

106 

9  651 

9  610 

+  41 

9  799 

-  148 

3.8 

149 

9  440 

9  476 

-   36 

9  648 

-  208 

3.9 

121 

9  488 

9  356 

+  132 

9  501 

-  13 

4.0 

132 

9  360 

9  249 

+  111 

9  358 

+   2 

4.1 

117 

9  120 

9  152 

-  32 

9  220 

-  100 

4.2 

96 

8  911 

9  064 

-  153 

9  085 

-  174 

4.3 

65 

9  154 

8  984 

+  170 

8  955 

+  199 

4.4 

46 

8  663 

8  910 

-  247 

8  828 

-  165 

4.5 

28 

9  089 

8  843 

+  246 

8  704 

+  385 

4  6 

10 

9  500** 

4  7 

10 

10  500** 

4.8 

6 

8  833** 

4.9 

2 

9  000** 

JT 

1 

11  000** 

147 

229 

Root  mean-square  error  

181 

317 

*From  Roberts,*  Table  XX. 

**Excluded  in  fitting  curves  and  computing  errors. 


RELATION  BETWEEN  FAT  CONTENT  AND  MILK  YIELD 


609 


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RELATION  BETWEEN  FAT  CONTENT  AND  MILK  YIELD 


611 


TABLE  13. — COMPARISON  OP  MEAN  MILK  YIELDS  AS  OBSERVED,  AND  AS  CALCU- 
LATED FROM  LOGARITHMIC  AND  CONSTANT  ENERGY  CURVES 

Brown  Swiss  Register  of  Production,  Jan.  1,  1922 
All  Long-Time  Records,  Age-Corrected 

(See  Table  12) 


t 

f 

M0 

M, 

D 

M. 

D 

2.945 

2 

16  500* 

3  345 

1 

11  500* 

3.445 

6 

14  500 

14  261 

+  239 

13  886 

+   614 

3.545 

17 

13  559 

13  835 

-   276 

13  663 

-    104 

3.645 

19 

13  184 

13  465 

-   281 

13  446 

-   262 

3.745 

32 

13  781 

13  143 

+   638 

13  236 

+   545 

3.845 

31 

12  984 

12  862 

+    122 

13  033 

-     49 

3.945 

43 

12  593 

12  616 

-     23 

12  835 

-   242 

4.045 

49 

12  398 

12  402 

-        4 

12  643 

-   245 

4.145 

35 

12-  329 

12  214 

+    115 

12  458 

-    129 

4.245 

34 

11  265 

12  051 

-    786 

12  277 

-1012 

4.345 

15 

13  233 

11  910 

+  1323 

12  103 

+  1130 

4.445 

9 

12  611 

11  787 

+   824 

11  932 

+  679 

4.545 

9 

11  389 

11  683 

-   294 

11  766 

-   377 

4.645 

4 

9  500 

11  595 

-2095 

11  605 

-2105 

4  .  84  o 

4 

10  500 

11  461 

-   961 

11  296 

-   796 

4.945 

1 

13  500 

11  414 

+  2080 

11   147 

+  2353 

Mean  error  

671 

709 

Root  mean-square  error  

947 

980 

*Ezcluded  in  fitting  curves  and  computing  errors. 


612 


BULLETIN  No.  245 


[June, 


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RELATION  BETWEEN  FAT  CONTENT  AND  MILK  YIELD 


613 


TABLE  15. — COMPARISON  OF  MEAN  MILK  YIELDS  AS  OBSERVED,  AND  AS  CALCU- 
LATED FROM  LOGARITHMIC  AND  CONSTANT  ENERGY  CURVES 

Holstein-Friesian  Advanced  Register,  Vols.  24-30 
All  Long-Time  Records,  Including  Reentries 

(See  Table  14) 


t 

f 

M0 

MI 

D 

Me 

D 

2.445 

2 

16  500* 

2.545 

5 

21  360* 

2.645 

21 

17  214 

17  667 

-  453 

17  212 

+       2 

2.745 

63 

17  595 

16  924 

+  671 

16  893 

+  702 

2.845 

112 

17  000 

16  365 

+   635 

16  586 

+  414 

2.945 

207 

15  355 

15  927 

-   572 

16  290 

-  935 

3.045 

318 

15  729 

15  576 

+    153 

16  005 

-   276 

3.145 

511 

15  273 

15  289 

-      16 

15  730 

-  457 

3.245 

650 

14  800 

15  053 

-    253 

15  463 

-   663 

3.345 

753 

15  028 

14  857 

+   171 

15  206 

-    178 

3.445 

675 

14  446 

14  694 

-   248 

14  956 

-   510 

3.545 

588 

14  840 

14  558 

+  282 

14  715 

+   125 

3.645 

485 

14  091 

14  446 

-   355 

14  482 

-   391 

3.745 

326 

14  009 

14  353 

-   344 

14  256 

-   247 

3.845 

222 

13  973 

14  278 

-   305 

14  037 

-      64 

3.945 

120 

14  475 

14  217 

+  258 

13  824 

+  651 

4.045 

71 

14  880 

14   170 

+  710 

13  618 

+  1262 

4.145 

64 

13  984 

14  135 

-   151 

13  418 

+   566 

4.245 

34 

15  617* 

4.345 

20 

18  050* 

4.445 

11 

14  318* 

4.545 

6 

19  000* 

4.645 

1 

18  500* 

4.945 

1 

9  100* 

Mean  error  

348 

465 

Root  mean-square  error  

401 

566 

*Excluded  in  fitting  curves  and  computing  errors. 


614 


BULLETIN  No.  245 


[June, 


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19SS3] 


RELATION  BETWEEN  FAT  CONTENT  AND  MILK  YIELD 


615 


TABLE  17. — COMPARISON  OP  MEAN  MILK  YIELDS  AS  OBSERVED,  AND  AS  CALCU- 
LATED FROM  LOGARITHMIC  AND  CONSTANT  ENERGY  CURVES 

Holstein-Friesian  Advanced  Register,  Vols.  18-24 
•  All  Long-Time  Records,  Including  Reentries 

(See  Table  16) 


t 

f 

M0 

M, 

D 

Me 

D 

2.545 

1 

13  500* 

2.645 

4 

15  000 

16  286 

-1286 

16  505 

-1505 

2.745 

4 

16  250 

15  856 

+  394 

16  199 

+     51 

2.845 

5 

17  100 

15  542 

+  1558 

15  905 

+  1195 

2.945 

24 

15  167 

15  286 

-    119 

15  621 

-   454 

3.045 

67 

15  321 

15  063 

+  258 

15  347 

-     26 

3.145 

95 

15  290 

14  863 

+  427 

15  084 

+   206 

3.245 

113 

14  385 

14  679 

-   294 

14  828 

-   443 

3.345 

148 

14  264 

14  507 

-   243 

14  581 

-   317 

3.445 

132 

14  182 

14  344 

-    162 

14  342 

-    160 

3.545 

133 

13  816 

14   188 

-   372 

14   111 

-   295 

3.645 

89 

13  938 

14  039 

-    101 

13  887 

+     51 

3.745 

72 

12  583 

13  895 

-1312 

13  671 

-1088 

3.845 

44 

13  704 

13  755 

-     51 

13  460 

+   244 

3.945 

36 

13  890 

13  618 

+  272 

13  256 

+  634 

4.045 

12 

14  750 

13  485 

+  1265 

13  059 

+  1691 

4.145 

12 

13  083 

13  355 

-   272 

12  867 

+  216 

4.245 

6 

15  000* 

4  345 

2 

13  000* 

4.445 

4 

14  750* 

Mean  error  

524 

536 

Root  mean-square  error  

720 

746          V 

*Excluded  in  fitting  curves  and  computing  errors. 


616 


BULLETIN  No.  245 


[June, 


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RELATION  BETWEEN  FAT  CONTENT  AND  MILK  YIELD 


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618 


BULLETIN  No.  245 


[June, 


TABLE  20. — COMPARISON  OF  MEAN  MILK  YIELDS  AS  OBSERVED,  AND  AS  CALCU- 
LATED FROM  LOGARITHMIC  AND  CONSTANT  ENERGY  CURVES 

Holstein-Friesian  A.  R.  O.  Seven-Day  Records 
First  277  Original  Entries,  Age-Corrected 

(See  Table  19) 


f 

M0 

M, 

D 

M. 

D 

2.145 

1 

625.0* 

2.345 

1 

525.0 

534.4 

-  9.4 

526.5 

-    1.5 

2.445 

1 

475.0 

521.3 

-46.3 

516.2 

-41.2 

2.545 

2 

600.0 

509.4 

+90.6 

506.2 

+93.8 

2.645 

6 

491.7 

498.5 

-  6.8 

496.7 

-   5.0 

2.745 

12 

487.5 

488.4 

-  0.9 

487.5 

0.0 

2.845 

22 

477.3 

478.9 

-    1.6 

478.6 

-   1.3 

2.945 

24 

487.5 

470.1 

-1-17.4 

470.1 

+  17.4 

3.045 

30 

460.0 

461.8 

-   1.8 

461.9 

-   1.9 

3.145 

32 

450.0 

454.1 

-   4.1 

453.9 

-  3.9 

3.245 

28 

442  9 

446.9 

-   4.0 

446.2 

-  3.3 

3.345 

22 

436.4 

440.0 

-   3.6 

438.8 

-  2.4 

3.445 

22 

434  1 

433.5 

-1-  0.6 

431.6 

+  2.5 

3.545 

20 

415.0 

427.4 

-12.4 

424.6 

-  96 

3.645 

14 

421.4 

421.6 

-   0.2 

417.9 

+  3.5 

3.745 

8 

412.5 

416.1 

-   3.6 

411.4 

+  1-1 

3.845 

7 

396.4 

410.8 

-14.4 

405.1 

-  8.7 

3.945 

8 

412.5 

405.8 

+  6.7 

3»8.9 

+  13.6 

4.045 

6 

391.7 

401.1 

-  9.4 

393.0 

-   1.3 

4.145 

2 

425.0 

396.5 

+28.5 

387.2 

+37.8 

4.245 

4 

425.0 

392.2 

+32.8 

381.6 

+43.4 

4.345 

2 

350.0 

388.1 

-38.1 

376.2 

-26.2 

4.445 

2 

400.0 

384.1 

+  15.9 

370.9 

+29.1 

4.845 

1 

425.0* 

Mean  error  

15  9 

15  8 

Root  mean-«quare  error  

26.1 

27.0 

•Excluded  in  fitting  curves  and  computing  errors. 


19S3] 


RELATION  BETWEEN  FAT  CONTEXT  AND  MILK  YIELD 


619 


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620 


BULLETIN  No.  245 


[June, 


TABLE  22. — EQUATIONS  TO  FITTED  CURVES  EXPRESSING  RELATION  BETWEEN 
PERCENTAGE  FAT  CONTENT  AND  YIELD  OF  MILK 

(Y  =  yield  of  milk,  in  pounds;  t  =  percentage  fat  content  of  milk) 


REFERENCE  TO  — 

Y   : 

Logarithmic 
=  a  +  bx  +  c  logio 

(x  +  o) 

Constant 
energy 
a 

Constant 
fat 
a 

Fig. 
No. 

Table 
No. 

Records 

2.66+t 

t 

a 

b 

c 

a 

0 

a** 

a 

1 
8 

9 
10 

2 
3 
4 
5 
6 
7 

2 
15 

17 
20 

4 
6 
8 
9 
10 
13 

Holstein  C.T.A. 

10  732.0 
22  026.3 
16  645.7 

1  017.5 
6  952.4 
12  117.5 
430.9 
18  869.2 
13  039.9 

31  457.9 

-  38.95 
+  165.50 
-   88.50 

+     1.87 
-   36.80 
-  49.10 
-     1.71 
+   12.70 
+  28.00 

+249.10 

-   2  718.2 
-  8  317.2 
-   1  539.9 

-       442.3 
-       907.9 
-  2  530.2 
-         89.9 
-  7  482.2 
-  3  736.8 

-17  084.4 

5.5 
2.5 
.5 

11.5 
1.5 
3.5 
4.5 
9.5 
1.5 

9.5 

24.45 
25.45 
25.45 

<22.45 
36.45 
37.45 
35.45 
36.00 
29.00 

33.45 

43  548 
91  309 
87  559 

2  635 
41  432 
64  659 
2  227 
66  100 
62  325 

84  776 

24  909 
50  532 
48  457 

1  460 
27  087 
43  142 
1  457 
43  177 
36  091 

51  317 

Holstein-Friesian 
A.R.  (Vols.  24-30) 

Holstein-Friesian 
A.R.  (Vols.  18-24) 

Holstein-Friesian 
A.R.O.  (7-day), 
age-corrected.  .  .  . 
Jersey  C.T.A. 
(yearly)  

Jersey  R.M. 

Jersey  R.M. 
(7-day)*  

Guernsey  A.R. 

Ayrshire  A.R. 
(yearly)  

Brown  Swiss  R.P. 
(yearly),  age- 
corrected  

*The  records  of  cows  under  four  years  of  age  were  excluded  in  making  up 
this  correlation  table  because  the  entrance  requirement  (12  pounds  of  fat,  re- 
gardless of  age)  is  relatively  high  for  young  cows,  and  it  was  thought  this  might 
tend  unduly  to  exclude  cows  of  lower  fat  percentage  under  the  age  of  four  years. 

**This  constant  should  afford  an  equitable  physiological  basis  of  comparison 
for  the  production  of  the  groups  and  breeds.  The  data  have  not  been  treated 
with  this  object  in  mind,  however,  and  there  are  three  things  which  are  not  al- 
ways comparable,  viz.:  length  of  record,  age,  and  period  when  the  records  were 
made.  Judging  by  the  cow  testing  association  records,  the  values  of  a  indicate 
that  the  Jersey  is  95  percent  (41432/43548)  as  high  a  producer  as  the  Holstein. 
By  the  advanced  registry  records,  she  is  only  71  percent  (64659/91309)  as  high. 
Looked  at  in  another  way,  the  Jersey  advanced  registry  records  are  more  repre- 
sentative of  what  the  breed  does  under  commercial  conditions  than  is  the  case  with 
the  Holstein.  Comparing  all  the  breeds,  the  rank  in  descending  order  of  pro- 
duction is:  Holstein,  Brown  Swiss,  Guernsey,  Jersey,  and  Ayrshire.  This  sug- 
gests that  size,  rather  than  efficiency  of  the  mammary  apparatus,  may  be  the 
cause  of  that  rank. 


1923] 


RELATION  BETWEEN  FAT  CONTENT  AND  MILK  YIELD 


621 


TABLE  23. — ERRORS  OF  FITTED  CURVES 
(The  mean  error  is  given  first;  the  root  mean-square  error,  second) 


REFERENCE  TO  — 

TYPE  OF  CURVE 

Table 

No. 

Records 

Logarithmic 

Constant 
energy 

Constant 
fat 

2 

Holstein  OT.A  

248 
397 

249 
391 

555 

775 

15 

Holstein-Friesian  A.R.  (V.  24-30)  

348 
401 

465 
566 

1001 
1203 

17 

Holstein-Friesian  A.R.  (V.  18-24)  

524 
720 

536 
746 

981 
1355 

20 

Holstein-Friesian  A.R.  O.  (7-day)  

15.9 
26.1 

15.8 
27.0 

37.4 
49.6 

4 

Jersey  C.  T.  A  

323 
421 

329 
428 

426 
551 

6 

Jersey  R.M.  (yearly)  

439 
770 

457 
777 

498 

867 

8 

Jersey  R.M.  (7-day)  

10.4 
13.0 

10.4 
13.1 

16.1 
21.3 

9 

Guernsey  A.R  

331 
546 

349 
569 

386 
673 

10 

Ayrshire  A.R  

147 
181 

229 
317 

437 
521 

13 

Brown  Swiss  R.P  

671 
947 

709 
980 

772 
1101 

AUTHOR  INDEX 


623 


AUTHOR  INDEX 


Anderson,  H.  W.  Dendrophoma 
Leaf  Blight  of  Straw- 
berry   125-136 

Andrews,  J.  B.,  Handschin,  W.  F., 
and  Rauchenstein,  E.  The 
Horse  and  the  Tractor.  .169-224 

Carmichael,  W.  J.,  and  Bice, 
John  B.  Variations  in  Far- 
row :  With  Special  Reference 
to  the  Birth  Weight  of 
Pigs 65-96 

Davidson,  F.  A.,  and  Gaines, 
W.  L.  Relation  between  Per- 
centage Fat  Content  and 
Yield  of  Milk :  Correction  of 
Milk  Yield  for  Fat  Con- 
tent   575-622 

Dungan,  G.  H.,  Tisdale,  W.  H., 
and  Leighty,  C.  E.  Flag 
Smut  of  Wheat,  with  Special 
Reference  to  Varietal  Resist- 
ance   507-538 

Edmonds,  J.  L.,  and  Kammlade, 
W.  G.  Feeding  Pure-Bred 
Draft  Fillies 329-360 

Edmonds,  J.  L.,  and  Kammlade, 
W.  G.  Feeding  Farm  Work 
Horses  and  Mules 409-428 

Flint,  W.  P.,  and  Hackleman,  J. 
C.  Corn  Varieties  for  Chinch- 
Bug  Infested  Areas 539-550 

Gaines,  W.  L.,  and  Davidson, 
F.  A.  Relation  between  Per- 
centage Fat  Content  and 
Yield  of  Milk :  Correction  of 
Milk  Yield  for  Fat  Con- 
tent   575-622 

Hackleman,  J.  C.,  and  Flint,  W. 
P.  Corn  Varieties  for  Chinch- 
Bug  Infested  Areas 539-550 

Hall,  H.  F.,  Ross,  H.  A.,  and 
Rhode,  C.  S.  The  Feed  Cost 
of  Milk  and  Fat  Production 
as  Related  to  Yields 551-574 

Handschin,  W.  F.,  Andrews,  J.  B., 
and  Rauchenstein,  E.  The 
Horse  and  the  Tractor. .  .169-224 


PAGE 

Harding,  H.  A.  Effect  of  Tem- 
perature of  Pasteurization  on 
the  Creaming  Ability  of 
Milk 393-408 

Harding,  H.  A.,  and  Prucha,  M. 
J.  An  Epidemic  of  Ropy 
Milk 109-124 

Harding,  H.  A.,  and  Prucha,  M. 
J.  Elimination  of  Germs 
from  Dairy  Utensils.  I.  By 
Rinsing.  II.  By  Drying  in 
Sun  and  Air 137-168 

Harding,  H.  A.,  and  Ptucha,  M. 
J.  Germ  Content  of  Milk. 
III.  As  Influenced  by  Visi- 
ble Dirt 361-392 

Hopkins,  Cyril  G.  How  Greece 

Can  Produce  More  Food. 429-470 

Kammlade,  W.  G.,  and  Edmonds, 
J.  L.  Feeding  Pure-Bred 
Draft  Fillies 329-360 

Kammlade,  W.  G.,  and  Edmonds, 
J.  L.  Feeding  Farm  Work 
Horses  and  Mules 409-428 

Leighty,  C.  E.,  Tisdale,  W.  H., 
and  Dungan,  G.  H.  Flag 
Smut  of  Wheat,  with  Special 
Reference  to  Varietal  Resist- 
ance   507-538 

Mitchell,  H.  H.  A  Graphical 
Presentation  of  the  Financial 
Phases  of  Feeding  Experi- 
ments   269-328 

Pearson,  F.  A.  The  Seasonal 

Cost  of  Milk  Production..  .1-18 

Pearson,  F.  A.,  and  Ross,  H.  A. 
Comparative  Expense  of  Me- 
chanical and  Hand  Milk- 
ing ... 491-506 

Prucha,  M.  J.,  and  Harding, 
H.  A.  An  Epidemic  of  Ropy 
Milk 109-124 

Prucha,  M.  J.,  and  Harding, 
H.  A.  Elimination  of  Germs 
from  Dairy  Utensils.  I.  By 
Rinsing.  II.  By  Drying  in 
Sun  and  Air  .  ..137-168 


02-1 


AUTHOR  INDEX 


PAGE 

Prucha,  M.  J.,  and  Harding, 
H.  A.  Germ  Content  of  Milk. 
III.  As  Influenced  by  Visible 
Dirt 361-392 

Rhode,  C.  S.,  Ross,  H.  A.,  and 
Hall,  H.  F.  The  Feed  Cost 
of  Milk  and  Fat  Production 
as  Related  to  Yields 551-574 

Rice,  John  B.,  and  Carmichael, 
W.  J.  Variations  in  Farrow: 
With  Special  Reference  to 
the  Birth  Weight  of  Pigs.  .65-96 

Richmond,  Thomas  E.,  and  Whit- 
ing, Albert  L.  Sweet  Clover 
for  Nitrate  Production.  .253-268 

Ross,  H.  A.  The  Production  and 
Utilization  of  Manure  on 
Dairy  Farms 471-490 

Ross,  H.  A.,  and  Pearson,  F.  A. 
Comparative  Expense  of  Me- 
chanical and  Hand  Milk- 
ing   491-506 

Ross,  H.  A.,  Hall,  H.  F.,  and 
Rhode,  C.  S.  The  Feed  Cost 
of  Milk  and  Fat  Production 
as  Related  to  Yields. .. .551-574 


PAGE 

Schoonover,  Warren  R.,  and  Whit- 
ing, Albert  L.  Nitrate  Pro- 
duction in  Field  Soils  in 
Illinois 19-64 

Stewart,  Robert.  Sulfur  in  Rela- 
tion to  Soil  Fertility 97-108 

Tisdale,  W.  H.,  Dungan,  G.  H., 
and  Leighty,  C.  E.  Flag 
Smut  of  Wheat,  with  Special 
Reference  to  Varietal  Resist- 
ance   507-538 

Whiting,  Albert  L.,  and  Schoon- 
over, Warren  R.  Nitrate  Pro- 
duction in  Field  Soils  in 
Illinois 19-64 

Whiting,  Albert  L.,  and  Rich- 
mond, Thomas  E.  Sweet 
Clover  for  Nitrate  Produc- 
tion   253-268 

Division  of  Applied  Chemistry  of 
the  University  of  Illinois; 
the  Illinois  Geological  Sur- 
vey; and  the  Agricultural 
Experiment  Station  .  .  ..225-252 


INDEX 


fF-fAf625 


INDEX 


(The  headings  in  capitals  are  subjects  of  entire  bulletins) 


PAGE 

Acidity  of  soil  in  Greece 439-44 

and  plant  diseases 457 

Alhambra  experiment  field,  chinch- 
bug  damage 548-49 

Alsike  clover,  effect  of  potassium 

on  production 249 

Alunite,    potassium    supplied    by 

-. . . .  .244,  245,  247,  249,  250,  252 
Ammonia    in    soil    samples,    de- 
termination of 22 

Ascochyta  Fragariae 135 

Ayrshire     records,     relation     be- 
tween   fat    percentage    and 

milk  yield 589-90 

Bacteria,  see  Germs 

Barley,    effect    of    potassium    on 

production 249 

Bedding  for  draft  fillies 333 

Beets,  effect  of  potassium  on  pro- 
duction   249 

Bone    meal,    amount    applied    in 

nitrate  experiments 29 

Brown  Swiss  records,  relation  be- 
tween   fat    percentage    and 

milk  yield 590 

Buckwheat 

Effect  of  kainit  and  shale  on 

production 251 

Effect    of    potassium    on    pro- 
duction  247,   250,  252 

Effect  of  shales  on  growth.  .233-34 
Effect  of  various  fertilizers  on 

growth 246 

Butter  fat,  see  Fat 
Calculations  for  determining  cost 
of   gains   in   feeding   experi- 
ments   269-328 

Cement-making,  111.  shales  for...  230 
Chicago,  milk  filtration  tests  at.  370 
' '  Chilisaltpeter, ' '  see  Sodium 

nitrate 

Chinch-bugs,  corn  varieties  resist- 
ant to  539-50 

Clover 

Effect  of  potassium  on  produc- 
tion   247,  249 

Influence    on    nitrate    produc- 
tion       59 

Pot-culture     experiments    with 

potassium 245 

see  also  Melilotus ;  Sweet  clover 


PAGE 


Corn 

Effect  of  kainit  and  shale  on 

production 251 

Effect  of  potassium  on  produc- 
tion      247 

Effect  of  shale  on  production.   228 
Experiment  to  determine  nitro- 
gen production  in  soil  grow- 
ing        30 

Nitrate  needs 45-46 

Development  of  chincn-bug  re- 
sistant varieties 546-48 

Sweet  clover  as  fertilizer  for. .  267 
Corn  fodder,  effect  of  potassium 

on  production 250 

CORN     VARIETIES     FOR 
CHINCH-BUG    INFESTED 

AREAS 539-50 

Cost-accounting,    study    of    milk- 
production  1-18 

Cows,  see  Dairy  Cows 
Cream 

Distinction  between  layer  and 

line 397 

Effect  of  temperature  of  pas- 
teurization on 393-408 

Cropping,     influence     on     nitrate 

production 54-55,  60 

Dairy  cows 

Feed  costs 551-73 

Manure  production 477 

Milk  from  clean 371-73 

Milk  from  dirty 

373-74,  384-87,  391 

Dairy     farms,     production     and 

utilization  of  manure  on.  .471-90 
Dairy  utensils 

Treatment  of  milk  cans  during 
epidemic  of  ropy  milk. .  .118-19 

Washing 140-41 

DAIRY  UTENSILS,  ELIMINA- 
TION OF  GERMS  FROM   137-68 
by  drying  in  sun  and  air...  157-68 
by  rinsing  with  hot  water . .  142-56 
Dairying,  see  Milk  production 
DENDROPHOMA      LEAF 
BLIGHT      OF      STRAW- 

BERRY 125-36 

Dendrophoma.  obscurans 135 

DRAFT     FILLIES,     FEEDING 

PURE-BRED  .  ..329-60 


626- 


VOLUME  16 


PAGE 
Drainage,    loss    of    sulfur    from 

soil  by 104-06 

Experiment  fields,  see  names  of 

fields 

Fairfield  experiment  field,  chinch- 
bug  damage 549 

Farm  organization,  studies  in  111.  173 
Fat  content  of  milk,  relation  to 

yield  of  milk 575-622 

Fat  production 

Feed  consumed  as  related  to. 555-63 

Relative  feed  cost 563 

see  also  Feed  cost  of  milk  and 

fat  production 
Feed 

Quantity  as  related  to  butter  fat 

production 555-63 

Quantity     for     milk     produc- 
tion   8,  9,  10,  12,  15 

Variation  in  cost  for  milk  pro- 
duction   5,  8,  12 

significance 11 

FEED  COST  OF  MILK  AND 
FAT  PRODUCTION  AS 
RELATED  TO  YIELDS .  551-74 

Bibliography 573 

Conclusions 572 

Records  used 553-54 

Feeding,  Forced,  for  milk  produc- 
tion   570-71 

Feeding  Experiments,  a  Graphi- 
cal Presentation  of  the 

Financial  Phases  of 269-328 

Feeding  experiments 

Factors  in  determining  cost . . .   273 
Farm  work  horses  and  mules. 409-28 

Pure-bred  draft  fillies 329-60 

FEEDING     FARM     WORK 

HORSES   AND   MULES. 409-28 
Fillies,  see  Draft  fillies 
FINANCIAL     PHASES     OF 
FEEDING     EXPERI- 
MENTS,     A     GRAPHICAL 
PRESENTATION  .  .   ..269-328 
FLAG      SMUT      OF      WHEAT, 
WITH    SPECIAL    REFER- 
ENCE TO  VARIETAL  RE- 
SISTANCE    507-38 

Bibliography 538 

Control  of 519 

conclusions 537 

crop  rotation 521-22 

date  of  seeding 522-23 

seed  treatment 519-21 

Dissemination 516,  519 

Fungus 515-16 

Losses  due  to 513-14 

Occurrence 512-13 

Symptoms 514-15 

Flax,  effect  of  potassium  on  pro- 
duction .  .  249 


PAGE 

Food,   How   Greece   can  produce 

more 429-70 

Garget Ill 

Geneva  Exp.  Sta.,  experiment  to 
show  loss  of  sulfur  in  drain- 
age water 105 

Germs 

Elimination    from    dairy   uten- 
sils   ". 137-68 

Germ  content  of  milk 363 

Method  of  counting 141 

Ropy  milk 114-15 

Gestation  period  for  pigs. 68-69,  71,  77 
Graphical  methods   for  interpre- 
tation    of     feeding     experi- 
ments   270-328 

Greece 

Fertility  of  soils 440-49 

HOW    GREECE    CAN    PRO- 
DUCE MORE   FOOD 429-70 

Limestone  in 449-51 

Guernsey  records  showing  rela- 
tion between  fat  content  and 

milk  yield' 589 

Gypsum  as  fertilizer 99 

Hancock  co.,  111.,  Rainfall  varia- 
tion in 176 

Hart  and  Peterson  determine  sul- 
fur content  of  plants 100 

Holstein  Friesian  records  show- 
ing relation  between  fat  con- 
tent and  milk  yield 591-93 

Holstein  records  showing  relation 
between  fat  content  and  milk 

yield 584 

HORSE   AND   THE   TRACTOR, 

THE 169-224 

Horses 

Analysis   of  farm   horse-power 

requirements 202-09 

Cost  of  horse-labor 178-86,  221 

reducing  .  . 187-201 

Farm  operations  for. .  .203,  205-206 

Feed,  cost  of 419 

Feeding  experiments .  329-60,  409-27 
Fillies  used  in  feeding  experi- 
ments   339-47 

Manure  production 477 

Used  in  horse-labor  studies. ...   176 

Iron,  essential  plant  food 99 

Jersey  records  showing  relation 
between  fat  content  and  milk 

yield 585-86,  588-89 

Kainit,    potassium    supplied    by 

244,  245,  247,  249,  250,  251,  252 
Labor 

Amount  and  cost  of  caring  for 

cows  milked  mechanically . . .  502 
Amount   and  cost  for  milking 
497-98,  499,  502 


INDEX 


PAGE 

Cost  for  hauling  manure. . .  .487—89 
Quantity   for   milk   production 

8,  9,  10,  12,  15 

Variation  in  cost  for  milk  pro- 
duction   8,  12 

significance 11 

see  also  Horses,  cost  of  labor 

Land-plaster 99 

Leucite,    potassium    supplied    by 

244,  245,  247,  249,  250,  252 

Limestone 

Amount  applied  in  nitrate  ex- 
periments       29 

Analysis  by  farmers 452 

Effect    on    nitrate    production 

24,  27,  53-54 

In  Greek  soils 439-444 

In  soils 447-48 

Sources  in  Greece 449-451,  453 

Lupine  for  soil  improvement 457 

Lysimeter  experiment,  Cornell.  104-06 
MANURE,  THE  PRODUCTION 
AND     UTILIZATION     ON 
ILLINOIS  DAIRY  FARMS 

471-90 

Manure 

Amount   recovered   from   farm 

animals 475-78 

Crops  utilizing 480-82 

Green    compared    with    stable 

49,  59,  60 

Labor  cost  of  hauling 487-89 

Methods  of  utilizing 482-85 

Possible  rates  of  applying.  .478-80 

Seasonal  application 485-86 

Sweet  clover  as  green 255-56 

see  also  Organic  matter 
Melilotus  in  Greece 

Field  trials 462-64 

Grain  grown  after 459-62 

Nitrogen  in 456-57 

see  also  Sweet  clover 

Melilotus  alba 255 

Melilotus  indica 257 

Milk 

Dirt  in 364-369,  374-75 

Quality 139 

Seasonal  variation  in  price. .  .16-17 
MILK,  EFFECT  OF  TEMPER- 
ATURE OF  PASTEURIZA- 
TION ON  THE  CREAMING 

ABILITY  OF 393-408 

MILK,     AN     EPIDEMIC     OF 

ROPY 109-24 

MILK,    GERM   CONTENT    OF, 
AS     INFLUENCED     BY 

VISIBLE  DIRT 361-92 

Bibliography 390 

From  cleaned  cows 380-82 

From  dirty  cows 384-87 

Plan  of  experiment 371 


PAGE 
Relation   to   problem   of   clean 

milk 389 

Results  of  experiment 382-83 

Summary  and  conclusions 388 

When  ordinary  pail  was  used  378-80 
When    small-topped    pail    was 

used 375-78 

Milk  cans,  see  Dairy  utensils 
Milk  production 

Feed  consumed  as  related  to ...  563 

digestible  nutrients 564 

Forced  feeding  for 570-71 

Nutrients     required     for     100 

pounds 569 

Records  of   Holstein  cows 564 

MILK      PRODUCTION,      THE 

SEASONAL  COST  OF 1-18 

Conclusions 18 

Cow  cost  by  months 12-14 

Herd  cost  by  months 4—7 

MILK  YIELD,  RELATION  BE- 
T  W  E  E  N  PERCENTAGE 
FAT  CONTENT  AND.. 575-622 

Bibliography 598 

Coefficient   of   correlation 584 

Conclusions 598 

Correction  for  fat  percentage.  594 

Hypothesis  .  . 579-80 

Source  of  data 578-79 

Summary 597-98 

Milkers,    mechanical,    conclusions 

as  to  use 493 

MILKING,  COMPARATIVE 
EXPENSE  OF  MECHANI- 
CAL AND  HAND 491-506 

Bibliography 506 

Minonk  experiment  field,  experi- 
ment with  sweet  clover  for 

nitrate  production 261-62 

Mules,  feeding  experiments. .  .409-27 

Mycosphaerella  Fragariae 

127,  133,  135 

Newton  experiment  field,  experi- 
ment with  sweet  clover  for 

nitrate  production 264 

NITRATE  PRODUCTION,  IN 
FIELD  SOILS  IN  ILLI- 
NOIS   19-64 

Conclusions 60-61 

Factors  of  production 21,  22 

Methods  of  determination . . .  62-63 

Relative  rates 60-61 

Time  of  maximum 60 

Nitrate  production,  sweet  clover 

for 253-68 

Nitrogen 

Amount  needed  for  crops. .  .455-56 

Cost 455 

In    soils    of    America    and    of 

Greece 445-46 

Reduction  of  loss  by  leaching     61 


628 


VOLUME  16 


PAGE 

Source 456-57 

Utilization  by  crops 61 

see  also  Nitrate 
Oats 

Nitrate  needs 46-47 

Nitrate  production  in  soil  grow- 
ing       43 

Pot-culture    experiments    with 

potassium 245 

Oblong  experiment  field,  experi- 
ment with  sweet  clover  for 

nitrate  production 264-65 

Ohio  Exp.  Sta.,  experiment  to  test 

effect  of  sulfur  on  crops.  .102-03 

Oil  in  potash  shales 229 

Organic  matter,  value  in  nitrate 

production 35 

Osborne   method   of    determining 

sulfur  content  of  plants....   100 
Pasteurization 

As     protection     against     ropy 

milk 121-22 

EFFECT       OP       TEMPERA- 
TURE      ON       CREAMING 
ABILITY  OF  MILK... 393-408 
Establishment  of  temperatures 

for 396 

Pasture,  nutrients  obtained  from  567 
Pa.  Exp.  Sta.,  experiment  to  test 

effect  of  sulfur  on  crops. ...   102 

Phoma  obscurans 133,  134 

Phosphates,  see  Phosphorus ;  Rock 

phosphate 
Phosphorus 

In  soils 446 

Sources  of 454-55 

Value  in  nitrate  production 36 

Phyllosticta  fragaricola 132,  133 

Pigs,  birth  weight  of 65-96 

see  also  Swine 

PIGS,  VARIATIONS  IN  FAR- 
ROW: WITH  SPECIAL 
REFERENCE  TO  THE 

BIRTH  WEIGHT  OF 65-96 

Plants,  sulfur  requirements  of..   100 
Plowing,  see  Tillage 
Potash,  extraction  from  shales..   235 
POTASH    SHALES    OF    ILLI- 
NOIS   225-52 

Constitution 231-35 

Geology,  distribution  and  occur- 
rence in  Union  co 237-43 

Potassium 

In  soils 447,  458-59 

Pot-culture  experiments  with  on 

peaty  soils 245 

Shale  as  source  of 244-52 

Potassium   sulphate   as   fertilizer  103 
Rainfall,  sulfur  content  of 106-08 


PAGE 

Rape 

Effect  of  potassium  on  produc- 
tion    250 

Effect  of  shale  on  produc- 
tion   248,  249 

Residues,   value   for   nitrate   pro- 
duction in  soil 45 

Rock  phosphate 59,  60 

Amount  applied  in  nitrate  ex- 
periments    29 

Influence  on  nitrate  production     50 

Septoria  aciculosa ,  .   135 

Shales 

Analysis  of  Illinois 236 

As  source  of  potassium 244-52 

Character  in  Union  co 238-39 

Potash 229-36 

Smut,  Flag,  of  wheat 507-38 

Sodium  nitrate 

Cost 23 

Equivalent  in  nitrogen 28 

Soil 

Acidity 439,  444 

and  plant  diseases 457 

Analysis 439,  445 

Dead 458 

Difference  in 437-38 

Improvement,  proof  of 457-58 

Limestone  in 447-48 

Moisture  content  in  nitrate 
production  experiments  .... 
31,  33,  37,  39,  42,  44,  56,  57,  58 

method  of  determination 62 

Nitrogen  in 445—46 

Of  Greece 438-39,  440-44 

fertility 448^9 

Phosphorus  in 446 

Potassium  in 447 

Sulfur  content 100-01 

Sulfur  in  relation  to  fertility  97-108 

Testing  by  farmers 448 

Treatment    for    production    of 

nitrate 24,  60 

Soybeans,    influence     on    nitrate 

production 59 

Sows,  see  Pigs 

STRAWBERRY,       D  E  N  D  R  O- 
PHOMA     LEAF     BLIGHT 

OF 125-36 

Control 135-36 

Fungi 135 

History  of  disease 132-34 

Infection  experiments 131-32 

Isolation  and  cultural  charac- 
ters    129 

Morphology  and  life  history  129-31 

Symptoms 127-29 

Taxonomy 134-35 


INDEX 


629 


FAQS 

Sulfate   of   calcium   for   soil   im- 
provement       99 

Sulfur 

Content  of  Kentucky  soils 106 

Content  of  rainfall 106-08 

Effect  on  crop  production.  .101-04 

Loss  in  drainage  water 104-06 

Requirement   of   plants 100 

SULFUR    IN    RELATION    TO 

SOIL  FERTILITY 97-108 

Sweet  clover 

As  a  green  manure 255-257 

Effect  of  potassium  on  produc- 
tion    250 

Effect  of  shale  on  production  248 
Nitrogen  content  and 

weights 266-67 

Value  for  nitrate  production . .     45 
SWEET     CLOVER     FOR     NI- 
TRATE PRODUCTION..  253-68 
see  also  Melilotus 

Swine,  feeding  experiments. .  .283-84, 
289,   291-92,   293,   295,   298,   301 
see  also  Pigs 
Temperature,    effect    on    nitrate 

production 25-27 

Tillage  as  factor  in  nitrate  pro- 
duction   21,  24-25 

Toledo    experiment    field,    experi-    ' 
ment  with   sweet  clover  for 

nitrate  production 263 

Tractors 

Advantages  .  . 222 

Displacement  of  horses  by.. 221-22 


PAGE 

Farm  operations  for 

202,  203,  206,  208 

The  horse  and  the  tractor .  169-224 

Soil  preparation  by 224 

Survey  of  use 210-20 

Tricalcium  phosphate  for  soils. .     24 
Tuberculosis     germs     killed     by 

pasteurization    of   milk 396 

Urbana,  University  North  Farm 
Experiments   to    determine   ni- 
trate production 29-44 

Corn  crop 45-46 

Oat  crop 46-47 

Wheat  crop 46 

Experiments  with  sweet  clover 

for  nitrate  production . . .  259-261 
Urbana,  University  South  Farm, 
Experiments  to  determine  ni- 
trate   production 47,    59 

Urbana    experiment    field,    Corn 

variety  trials   549-50 

Urocystis  occulta 515 

tritici 511,  515,  527 

Wheat 

Effect  of  fertility  on . ..  437 

Flag  smut  of 507-38 

Necessity  for  Greece  to  raise. .  464 
Nitrate      production     in     soil 

growing 40 

Nitrogen  needs 46 

Pot-culture     experiments     with 

potassium 245 

Varietal     resistance     to     flag 

smut 523-37 

Yield  in  Greece  .  ,  .  .434-35 


